homework2 function&arrays
homework2
ExercisesPart one1. What is acoustic phonetics? [人大2003研]【答案】Acoustic phonetics is a technical area of linguistics. It is the study of sound waves made by the human vocal organs for communication.2. Auditory phonetics studies how sounds are perceived by the speaker.[清华2001研]【答案】FPart two:一、术语解释IPA [南开大学2004研]【答案】IPA: the abbreviation of International Phonetic Alphabet, which is devised by the International Phonetic Association in 1888. IPA is a set of symbols which can be used to represent the phones and phonemes of natural languages.二、简答题What are the three parts of the vocal organs (3 points)? [清华2001研]【答案】The pharynx, the mouth and the nose are the three parts of the vocal organs.三、论述题Is English a language that uses a phonetic alphabet system? Explain briefly why or why not with examples. (15 points) [北外2004研] 【答案】The Phonetic Alphabet is a system of letters and symbols that are used to represent the individual sounds of a language. English is a language that uses a phonetic alphabet system because it is a phonographic language by nature. There are mainly three types of language concerning its writing system: ideographic language which uses symbols (ideograms) to represent whole words or concepts (ideas), with Chinese as an example; syllabic language in which words or concepts are represented by syllable, with Japanese syllabic system as an example; phonographic language which uses special alphabetic or other typographical characters to express the sounds of an actual spoken utterance in writing, with many European languages as examples. English uses alphabetic script to represent certain single type sound. For example, the sound which is written as sh in English can be expressed by symbol [∫], as in ship; and the sound that is written as c can be expressed by the symbol of [k], as in cup.四、选择题Of the three cavities, is the most variable and active in amplifying and modifying speech sounds. [北京第二外国语学院2004研]A. nasal cavityB. pharynx cavityC. oral cavity【答案】C五、判断正误1. When the vocal folds are apart, the air can pass through easily and the sound produced is said to be voiced. [大连外国语学院2008研] 【答案】F2. Of the three cavities, pharynx cavity is the most variable and active in amplifying and modifying speech sounds. [北京第二外国语学院2007研]【答案】FPart three一、术语解释1. Cardinal vowel [四川大学2006研，大连外国语学院2008研] 【答案】The cardinal vowels are a set of vowel qualities arbitrarily defined, fixed and unchanging, intended to provide a frame of reference for the description of the actual vowels of existing languages.2. Glottal Stop [四川大学2006研]【答案】V ocal tract is composed of oral cavity, nasal cavity and pharynx. When the vocal folds are totally closed, no air can pass between them. The result of this gesture is the glottal stop.3. Bilabial consonant [四川大学2007研]【答案】Bilabial consonants refer to consonants which are made with the two lips.4. V oiceless [西安交通大学2008研]【答案】When the vocal folds are apart, the air can pass through easily and the sound produced is said to be voiceless. For example, consonants [p, s, t] are produced this way, so they are voiceless consonants. “V oiceless”is defined in contrast with “voiced”. Consonants [b, z, d] are voiced consonants.二、简答题1. Mention a labiodental sound in English. Tell what speech organs are involved in producing labiodental sounds. (4 points) [北京第二外国语学院2007研]【答案】/f/ (or /v/), the upper front teeth and the lower lip are involved.2. What are the differences between voiced sounds and voiceless sounds in terms of articulation? [南开大学2004研]【答案】When the vocal cords are spread apart, the air from the lungs passes between them unimpeded. Sounds produced in this way are described as voiceless. Consonants [p, s, t] are produced in this way. When the vocal cords are drawn together, the air from the lungs repeatedly push them apart as it passes through, creating a vibration effect. Sounds produced in this way are described as voiced. [b, z, d] arevoiced consonants.三、选择题1. Of the consonants /p/, /t/, /k/, /f/, /m/, /z/ and /g/, which has the features of voiceless and velar? [对外经济贸易大学2005研]A. /k/B. /p/C. /g/D. /t/【答案】A2. The vowel is a low back vowel. [西安外国语学院2006研]A. /i:/B. /u/C. /æ/D. /a:/【答案】D3. Point out which item does not fall under the same category as the rest, and explain the reason in ONE sentence. [南京大学2008研] A. /f/ B. /z/ C. /v/ D. /k/ [Focus on manner of articulation]【答案】D (Reason: A, B and C are fricatives, but D is a plosive.)五、填空题1. Consonant articulations are relatively easy to feel, and as a result are most conveniently described in terms of place and of articulation. [北京第二外国语学院2008研]【答案】manner2. are produced by constricting or obstructing the vocal tract at some place to divert, impede, or completely shut off the flowof air in the oral cavity. [中山大学2006研]【答案】consonants六、判断正误1. Bilabial consonant is produced when the obstruction is partial and the air is forced through a narrow passage. [对外经济贸易大学2006研]【答案】F2. The sound segments are grouped into consonants and vowels. [大连外国语学院2008研]【答案】T七、音标题Work out the distinctive features of the following sounds. (10%)[南开大学2007研]1.[t h]2.[w]3.[v]4.[ð]5.[l]【答案】1. [t h] aspirated voiceless alveolar stop2. [w] voiced bilabial approximant3. [v] voiced labio-dental fricative4. [ð] voiced dental fricative5. [l] voiced alveolar lateral一、术语解释1. Phoneme [人大2006研，浙江大学2005研，上海交通大学2007研]【答案】Phoneme refers to the abstract element of sound, identified as being distinctive in a particular language. For example, in English, /p/ is described as a phoneme.2. Minimal pairs [武汉大学2005研，浙江大学2004研，四川大学2007研，上海交通大学2006研，北京航空航天大学2008研，北京第二外国语学院2006研]【答案】Two words which are identical in every way except for one sound segment that occurs in the same place in the string. For example, the English words bear and pear constitute a minimal pair as they differ in meaning and in their initial phonemes /b/ and /p/. 3. Free variation [武汉大学2004研]【答案】Free variation is the interchangeable relationship between two phones, in which the phones may substitute for one another in the same environment without causing a change in meaning. For example, the final consonant of cup may not be released by some speakers so there is no audible sound at the end of this word. In this case, it is the same word pronounced in two different ways : [kʰʌpʰ]and [kʰʌp] (The diacritic “┐”indicates “no audible release ” in IPA symbols.)4. Allophone [四川大学2008研，北京交通大学2007研]【答案】Allophone refers to variants of the same phoneme, which are in complementary distribution and bear phonetic similarity.5. Coarticulation[武汉大学2008研，四川大学2006研，南开大学2007研]【答案】Coarticulation refers to the phenomenon that sounds continually show the influence of their neighbors. For example, in lamb, when a is followed by m, the velum will begin to lower itself during the articulation of a so that it is ready for the following nasal. When such simultaneous or overlapping articulations are involved, we call the process coarticulation. If the sound becomes more like the following sound, it is known as anticipatory coarticulation. If the sound displays the influence of the preceding sound, it is perseverative coarticulation.6. Broad and narrow transcription [中山大学2006研]【答案】When we use a simple set of symbols in our transcription, it is called a BROAD TRANSCRIPTION. And the use of more specific symbols to show more phonetic detail is referred to as a NARROW TRANSCRIPTION. Both are phonetic transcriptions so we put both forms in square brackets [ ].7. Complementary distribution [武汉大学2008研，南开大学2007研]【答案】When two sounds never occur in the same environment, they are in complementary distribution. For example, the aspirated English stops never occur after [s], and the unaspirated ones never occur initially. Allophones of the same phoneme are usually in complementary distribution. The allophones of /p/, for instance, are also in complementary distribution. The unaspirated [p] occurs after /s/, while the aspirated [ph] occurs in all other environments except after /s/.二、论述题What are phonemes, phones and allophones? Explain their relationship with examples from English or Chinese. (15 points) [北外2005研]【答案】A phoneme is a minimally distinctive set of sounds in a language that can signal a difference in meaning. It is an abstract phonological unit represented or realized by a certain phone in a particular phonetic context. A phone is an individual phonetic unit or segment that occurs in speech. The speech sounds we hear and produce during linguistic communication are all phones. Each of the set of phones which correspond to a single phoneme of a language is called an allophone. Phonemes are placed between slant lines (/ /)and phones are placed between square brackets ([ ]). Allophones of the same phoneme generally occur in different contexts and never distinguish one word from another. For example, when we pronounce the two words peak and speak, we are aware that the sound [p] is pronounced differently, in the word peak, it is pronounced with a strong puff of air stream; but the same stop sound is pronounced slightly differently in the word speak, where the puff of air is withheld a little. The [p] sound in peak is called an aspirated [ph] and the [p] sound in speak is an unaspirated [p]. There is a slight difference in the way they are pronounced, but such a difference does not give rise to difference in meaning. So /p/ is a phoneme in the English sound system, and it can be realized differently as aspirated or unaspirated in different contexts. The phoneme /p/ in English can be realized as aspirated [ph] and unaspirated [p], which are allophones of the phoneme /p/.三、选择题1. Which of the following is true of an allophone? [对外经济贸易大学2005研]A. A phone can be the allophone of all English vowel phonemes.B. There are no restrictions on the distribution of an allophone.C. There is no possibility of an allophone becoming a phoneme.D. An allophone changes the meaning of the word.【答案】C2. Which of the following CANNOT be considered as minimal pair? [大连外国语学院2008研]A. /ai/-/ɔi/B. /p/-/b/C. /s/-/θ/【答案】C3. Point out which item does not fall under the same category as the rest, and explain the reason in ONE sentence. [南京大学2007研] A. resolution B. resident C. restart D. resignation [Focus on the pronunciation of “s”]【答案】C ( Reason: in A, B, D, “s”are all pronounced as [z], while in C “s”is pronounced as [s].)四、填空题transcription should transcribe all the possible speech sounds, including the minute shades.[北京第二外国语学院2004研]【答案】narrow五、判断正误1. A phoneme in one language or one dialect may be an allophone in another language or dialect. [清华2000研，清华2001研] 【答案】T2. Broad Transcription is intended to symbolize all the possible speech sounds, including the minute shades. [北京第二外国语学院2003研]【答案】F3. Phonetic similarity means that the allophones of a phoneme must bear some morphological resemblance. [大连外国语学院2008研]【答案】F补充：此题型还常考free variation和complementary distribution，phone和phoneme的区别。
homework的用法和搭配
homework的用法和搭配一、homework的含义与作用在学生的日常学习中，homework是一个常见的词汇。
它可以指代老师布置给学生在家完成的任务，也可以包括课外阅读、练习题或复习等活动。
作为教育系统中不可或缺的环节之一，做好homework对于学生个人发展和提升学业成绩具有重要意义。
1.1 提高自主学习能力完成homework需要学生在独立思考和解决问题方面付出努力。
通过独自处理问题并找到正确答案，他们培养了自主学习的能力。
这种能力使得学生更加独立，自信地应对各种挑战，并为将来的职业生涯做好准备。
1.2 强化概念理解和知识掌握通过consistently坚持做homework，学生有机会巩固他们在课堂上所学到的知识。
通过反复练习和应用，他们更容易掌握各种概念，并建立起良好的基础知识体系。
这将有助于他们更深入地理解所学内容，并在考试或其他评估中表现出色。
1.3 培养时间管理和组织技能homework可以帮助学生学会合理安排时间，并培养出良好的自我管理和组织能力。
通过完成deadline，学生将逐渐知晓如何高效地规划自己的工作和任务。
二、homework的搭配用法2.1 做（do）homework这是最常见的表达方式。
当老师布置了一项任务后，学生需要回家做（do）他们的homework。
这意味着他们需要在规定的时间内完成该项任务，并尽力解答问题或完成相应内容。
2.2 完成（finish）homework这是指学生确保所有作业都已经被正确完成的意思。
无论是写作业、做数学题还是准备演讲稿等，当学生把所有要求都满足并按时交给老师时，我们可以说他们已经完成（finish）了他们的homework。
2.3 交（hand in）homework当同学们做完了功课后，他们需要将其交给老师进行批改和评估。
在这种情况下，我们可使用动词短语“hand in”来描述此过程。
也有一些老师采用电子形式收取作业，那么可以使用“submit”或“submit the homework”。
Homework_2
Email or submit the three files: "hm2a.sh", "hm2b.sh", "typescript".
The file "typescript" is created by following the below command sequence:
4) Assign value to a variable, then display the content of the variable.
5) Create one function and make a call to the function.
After you finished questions 2) through 5) in the script "hm2b.sh", Use
Create another Shell script file "hm2b.sh" and do the following:
2) Include two commands with one pipe.
3) Perform one redirection with a command of your choice.
script
./hm2a.sh
./hm2b.sh
Ctrl-D
more typescript
Notes:
When you type script command, everything you type on keyboard and all
homework 2
南京，她有层出不穷的风流人物和彪炳千秋的不朽业绩。
大都会特有的凝聚力，吸引了无数风云人物、仁人志士在这里角逐争雄，一逞豪彦。
巍巍中山、滚滚长江养育了他们，为他们提供了施展抱负的舞台，他们也以自己的雄才大略、聪明智慧为中华民族的灿烂文明增添了流光溢彩的新篇章。
傅茂竹：Great men and immortal achievements emerged endlessly in Nanjing. A great number of famous persons and people with lofty ideals entered into rivalry to show their ability here because the cohesion of metropolis. The towering Zhongshan and the billowing Yangtze River nurtured them and provided them with stage for fulfilling their dreams. Their bold strategy and sagacity added a brightest chapter for our Chinese civilization.高娟霞：Nanjing, she has endless romantic characters and immortal performance to shine forever. As a Metropolitan, whose proper cohesion, attracted numerous person of the hour and lofty ideals here to compete for supremacy. And they, raised by lofty Zhongshan as well as the rolling Yangtze river, providing a stage for realizing their aspirations, also added a gleaming new chapter with their own outstanding ability and wisdom for the Chinese nation splendid civilization.综合：Great men and immortal achievements emerged endlessly in Nanjing. Attracted by her cohesion, a great number of famous persons and people with lofty ideals entered into rivalry to give play to their genius and virtues. The towering Zhongshan and the billowing Yangtze River nurtured them and provided them with a stage for realizing their aspirations. Furthermore, their own outstanding ability and wisdom added a gleaming new chapter for the Chinese nation splendid civilization.。
小学上册第十五次英语第二单元暑期作业(有答案)
小学上册英语第二单元暑期作业(有答案)英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.My mom is a ______. She helps us with homework.2.The _____ (露水) in the morning helps hydrate the plants.3.The ______ (花瓣的颜色) can signal to pollinators.4.The cat climbed up the ______.5.The main function of lipids is to store _____.6.The boy likes ________.7.The ________ is a tiny creature that makes music.8.The squirrel collects _______ (坚果) in the fall.9.The train travels ________ the city.10.We have ______ (一个) fun day at the amusement park.11.The __________ (历史的构成) is made up of many elements.12.The ocean is very _______ (广阔的).13.My family travels to ______ (不同的) places.14.The ________ is a joyful little animal.15.Many cultures celebrate the __________ (植物的生长季节).16.What is the name of the famous American author who wrote "To Kill a Mockingbird"?A. Harper LeeB. F. Scott FitzgeraldC. Ernest HemingwayD. Mark Twain答案:A17.The ________ is a famous ancient structure in India.18. A ________ (水獺) loves to swim and catch fish.19.The main gas produced in respiration is _____.20.My hamster runs on its _______ (运动) wheel.21.The first African American to serve as president was _______ Obama.22.The balloons are ___ (floating) in the air.23.In a biochemical reaction, enzymes act as biological _____ to speed up the reaction.24.My birthday is in _______ (九月).25. A chemical reaction can change the properties of ______.26.The cat is ______ on the couch. (sitting)27.The _______ (海豚) is very friendly.28.The girl is very ________.29.The __________ (分子量) is the sum of the atomic weights of all atoms in a molecule.30.I enjoy playing with my ________ (玩具名称) outside.31.What do we call the study of plants?A. BiologyB. BotanyC. ZoologyD. Ecology答案:B.Botany32.Acids tend to turn blue litmus paper _____.33.We write with a ___. (pen)34.My ________ (玩具) is made of eco-friendly materials.35.Astronomical observations have been made for thousands of ______.36.I find ________ (心理学) fascinating.37.The _____ (bicycle/car) is fast.38. A ________ (植物研究支持) fosters innovation.39.The manatee is often called a sea ________________ (牛) due to its gentle nature.40.__________ (表面张力) affects how liquids behave in different environments.41.The _____ (小动物) find shelter among the plants.42.The weather is _______ for a picnic.43.The process of breaking down food in our bodies releases _____.44.The _____ is the force that keeps the planets in orbit.45.The duckling follows its _______ (母亲) everywhere.46.The ________ (discussion) promotes understanding.47.I think it’s important to ________ (关心他人).48.What do you call the action of making a decision?A. DecidingB. ChoosingC. SelectingD. Picking答案: A49.The kids are _____ in the classroom. (talking)50.My mom enjoys __________ on weekends. (购物)51.I enjoy _______ (与家人一起)过周末.52.I enjoy going ________ (跑步) in the morning.53. A ______ (蜥蜴) can be green or brown.54.What do we call the distance around a circle?A. RadiusB. DiameterC. CircumferenceD. Area答案:C. Circumference55.The _____ (teacher/student) is helpful.56.I like to play ________ (排球) with my classmates.57.The __________ (非洲殖民时期) changed many countries.58.The girl sings very ________.59.I use my __________ (玩具名) to help me __________ (动词).60.We are going to the ___. (park)61.The _______ (小果子狸) has a long tail and is very agile.62.I like to collect __________ (玩具名) from different __________ (国家).63.I love to _______ (draw) pictures.64.What is the name of the famous landmark in Egypt?A. Great PyramidB. ColosseumC. Taj MahalD. Stonehenge答案: A65.My friend is very __________ (有耐心).66.The celestial sphere is useful for visualizing ______.67.The ________ (兰花) is a beautiful flower that comes in many colors.68.The ______ is the part of the plant that absorbs sunlight.69.The capital of Germany is __________.70.My brother is very ________.71. A period in the periodic table represents elements with the same number of ______.72. A chemical reaction that produces light and heat is called a ______ reaction.73.The balloon is ______ (yellow) and orange.74.They are friends from ________ (学校).75. A ______ is an animal that can be found in wetlands.76. A ______ (蜜蜂) moves from flower to flower gathering nectar.77.The __________ helps to shape the planet's climate.78.What is the capital of Jamaica?A. KingstonB. Montego BayC. Ocho RiosD. Mandeville答案:A.Kingston79.I have a toy _______ that dances and sings catchy tunes.80.I have a ______ of crayons. (box)81.How many wheels does a bicycle have?A. TwoB. ThreeC. FourD. Five答案:A82. A chemical equation uses symbols to represent a _____.83.What do we call a person who studies the relationship between biology and culture?A. Biocultural AnthropologistB. SociologistC. AnthropologistD. Historian答案: A84. A _______ can be a great project for kids.85. A wave can travel through solids, liquids, and ______.86.The monkey is ________ in the tree.87.The __________ is known for its historical significance.88. A chameleon can change to match its ________________ (环境).89.Burning wood produces __________.90.We have fun playing with ________ (玩具名称).91.The cat caught a ______.92.I love to help my parents ______.93.I enjoy watching a _______ (小金鱼) swim in its bowl.94.The chemical symbol for silver is ______.95. A ______ is a homogeneous mixture of two or more substances.96.Electrons are negatively charged ______ in an atom.97.The _____ (青蛙) has smooth skin and long legs.98.I love ________ with my family.99.The __________ is a region known for its beautiful beaches.100.The chemical formula for sodium bicarbonate is ______.。
function的概念
function的概念在计算机编程中，"function"（函数）是一种用于执行特定任务的独立代码块。
函数通常接受输入（称为参数），执行一系列操作，然后产生输出（称为返回值）。
函数的主要目的是将程序分解为更小的可管理单元，以便提高代码的可读性、可维护性和重用性。
以下是关于函数的一些基本概念：函数定义：函数通过定义来创建。
定义包括函数的名称、参数列表、函数体和返回类型（如果有的话）。
在许多编程语言中，函数的定义通常以关键字（例如，function、def、fun等）开始，后面是函数名和括号内的参数列表。
# 一个简单的函数定义（Python）def greet(name):return "Hello, " + name + "!"函数调用：在程序的其他地方，通过函数名和合适的参数列表来调用函数。
调用函数时，程序执行函数体内的代码。
# 调用上述定义的函数result = greet("John")print(result) # 输出: Hello, John!参数：函数可以接受零个或多个参数。
参数是传递给函数的值，函数在执行时可以使用这些值。
def add(a, b):return a + bresult = add(3, 5)print(result) # 输出: 8返回值：函数可以返回一个值，也可以没有返回值。
返回值是函数执行后产生的结果，可以在调用函数的地方使用。
def square(x):return x * xresult = square(4)print(result) # 输出: 16函数的重用：通过将功能封装在函数中，可以轻松地在程序的不同部分重用代码。
这提高了代码的可维护性和可读性。
def print_greeting(name):print("Hello, " + name + "!")print_greeting("Alice")print_greeting("Bob")局部变量和全局变量：函数内部定义的变量称为局部变量，只在函数内部可见。
哈工大人工智能原理习题homework-2
人工智能原理 练习题-2从习题中选择自己感兴趣的题目进行思考和解答，任何尝试都是有益的。
必要时，仔细阅读教科书当中的某些章节。
对于加星号的习题，应该编写程序来完成。
第3章 逻辑与推理1 对于下列每对原子语句，请给出最一般合一者，如果存在的话：a. (,,),(,,)P A B B P x y zb. (,(,)),((,),)Q y G A B Q G x y yc. ((),),((),)Older Father y y Older Father x Johnd. ((),),(,)Knows Father y y Knows x x2 写出下列语句的逻辑表示，使得它们适合应用一般化分离规则：a. 马、奶牛和猪都是哺乳动物。
b. 一匹马的后代是马。
c. Bluebeard 是一匹马。
d. Bluebeard 是Charlie 的父亲。
e. 后代和双亲是逆关系。
f. 每个哺乳动物都有一个双亲。
3 请根据第二章列出的任务环境特征描述wumpus 世界。
1，42，43，44，41，3 w ！2，33，34，31，2 S OK 2，2OK3，24，21，1 V OK 2，1B V OK3，1 P ！4，1A图7.4（a ） 智能体取得进展的两个后续函数。
（a ）第三步移动之后，感知为[Stench,None,None,None];A = AgentB = BreezeG = Gllitter,GoldOK = Safe squareP = PitS = StenchV = Visited W= WumpusA4 假定智能体已经前进到图7.4（a）（如上图）所示的位置，感知到的情况为：[1，1]什么也没有，[2，1]有微风，[1，2]有臭气。
它现在想知道[1，3]、[2，2]和[3，1]的情况。
这3个位置中的每一个都可能包含陷阱，而最多只有一个可能有wumpus。
按照图7.5的实例，构造出可能世界的集合。
中考英语复合句高级特殊情况练习题30题
中考英语复合句高级特殊情况练习题30题1<背景文章>Tom is a middle school student. He is currently studying complex sentences and finds himself in a bit of a dilemma. He is struggling to understand the advanced special cases of complex sentences. For example, when he encounters sentences with multiple clauses and different types of conjunctions, he often gets confused.One day, he was doing his English homework. The task was to analyze a complex sentence: “Although he is tired, ___ he still insists on finishing his homework.” Tom was not sure which word to fill in the blank. He thought about it for a long time and considered several options.He also found it difficult to distinguish between different types of complex sentences. For instance, he wasn't sure when to use “because” and when to use “since” in a sentence. He realized that understanding these advanced special cases of complex sentences is crucial for his English learning.Tom decided to ask his teacher for help. His teacher patiently explained the differences and gave him some examples. After listening to his teacher's explanation, Tom started to understand a little better. However, he still needs more practice to fully master these complex sentencestructures.1. In the sentence “Although he is tired, ___ he still insists on finishing his homework.”, which word should be filled in the blank?A. butB. soC. andD. yet答案：D。
离散数学习题及答案02
CIS 607: Mathematical Basis for ComputingSOLUTIONS OF HOMEWORK 2Homework 2 – Sets, Functions and RelationsDue Date: March 9, 2017In this homework, you will answer the following questions. Prepare a pdf file for your solutions and upload that pdf file into the blackboard system.Q1)a) Find the power set of each of these sets, where a and b are distinct elements.∙{a, b, c}→ PS({a,b,c}) = {∅, {a},{b},{c},{a,b}{a,c},{b,c},{a,b,c}}∙{∅, {∅}}→ PS({∅, {∅}}) = {∅, {∅},{{∅}},{∅,{∅}}}b)Find A3 if∙ A = {a}.→ A3 = {(a, a, a)}∙ A = {0, a}.→ A3 = {(0, 0, 0), (0, 0, a), (0, a, 0), (0, a, a), (a, 0, 0), (a, 0, a), (a, a, 0), (a, a, a)}c) Cardinalities of Cartesian products.∙How many different elements does A × B have if A has m elements and B has n elements?→ mn∙How many different elements does A × B × C have if A has m elements, B has n elements, and C has p elements?→ mnp∙How many different elements does A n have when A has m elements and n is a positive integer?→ m nQ2)a)Let A, B, and C be sets. Show that_________ _ _ _∙ A ∩ B ∩ C = A ∪ B ∪ C→Suppose that x in the left side.x ∉A ∩ B ∩ Cx ∉ A or x ∉ B or x ∉ Cx in the right side.←Suppose that x in the right side.x is not in A, or x is not in B or x is not in C.So, x is not in A ∩ B ∩ CSo, x is the left side.∙(A − B) − C ⊆ A – CSuppose that x ∈ (A − B) − C.Then x is in A−B but not in C.Since x ∈A−B, we know that x ∈ A.Since we have established that x ∈ A but x ∉C, we have proved that x ∈A − C.∙(A − C) ∩ (C − B) = ∅To show that the set given on the left-hand side is empty, it suffices to assume that x is some element in that set and derive a contradiction, thereby showing that no such x exists.So suppose that x ∈(A−C) ∩(C −B).Then x & A − C and x & C − B. The first of these statemen ts implies by definition that x ∉C, while the second implies that x ∈ C.This is impossible, so our proof by contradiction is complete.∙(B − A) ∪(C − A) = (B ∪C) − A.To establish the equality, we need to prove inclusion in both directions.To prove that (B − A)∪(C −A) ⊆(B ∪C) − A, suppose that x ∈(B − A) ∪(C − A).Then either x ∈(B − A) or x ∈(C − A).Without loss of generality, assume the former (the proof in the latter case is exactly parallel.) Then x ∈ B and x ∉A.From the first of these assertions, it follows that x ∈ (B ∪ C).Thus we can conclude that x ∈ (B ∪C) − A, as desired.For the converse, that is, to show that (B ∪C) − A ⊆(B − A) ∪(C − A),So, suppose that x ∈ (B ∪C) − A.This means that x ∈ (B ∪C) and x ∉ A.The first of these assertions tells us that either x ∈ B or x ∈ C.Thus either x ∈B − A or x ∈C − A. In either case, x ∈(B − A) ∪(C − A).b) What can you say about the sets A and B if we know that∙ A ∪ B = A?→ B ⊆ A∙ A ∩ B = A?→ A ⊆ B∙ A − B = A?→ A ∩ B = {}∙ A − B = B − A?→ A = Bc) Find ⋃A i ∞i=1 and ⋂A i ∞i=1if for every positive integer i,∙ A i = {i, i + 1, i + 2, . . .}. →⋃A i ∞i=1 = Z + (the set of positive integers) ⋂A i ∞i=1= ∅∙ A i = {0, i}.→⋃A i ∞i=1 = N (the set of natural numbers) ⋂A i ∞i=1= {0}∙ A i = (0, i), that is, the set of real numbers x with 0 < x < i.→ ⋃A i ∞i=1 = R + (the set of positive real numbers)⋂A i ∞i=1= (0, 1) (the interval of all real numbers between 0 and 1, exclusive)∙ A i = (i,∞), that is, the set of real numbers x with x > i.→ ⋃A i ∞i=1 = (1,∞) (all real numbers greater than 1).) ⋂A i ∞i=1= ∅a)Determine whether each of these functions from Z to Z is one-to-one and/or onto.∙ f (n) = n − 1This is one-to-one. This is onto.∙ f (n) = n2 + 1This is NOT one-to-one. This is NOT onto.∙ f (n) = n3This is one-to-one. This is NOT onto.∙ f (n) = ⌈n/2⌉This is NOT one-to-one. This is onto.b) Give an example of a function from N to N that is∙one-to-one but not onto.f(n) = n + 5∙onto but not one-to-one.f (n) = ⌈n/2⌉∙both onto and one-to-one (but different from the identity function).We let f(n) = n − 1 for even values of n, and f(n) = n + 1 for odd values of n.Thus we have f(1) = 2, f(2) = 1, f(3) = 4, f(4) = 3, and so on. Note that this is just one function, even though its definition used two formulae, depending on the the parity of n.∙neither one-to-one nor onto.f(n) = 5c) Determine whether each of these functions is a bijection from R to R.∙ f (x) = −3x + 4This is a bijection since the inverse function is f−1(x) = (4 − x)/3.∙ f (x) = −3x2 + 7This is NOT a bijection since it is not one-to-one ( f(1) = f(−1) ).∙ f (x) = (x + 1)/(x + 2)This is NOT a bijection since -2 is not in its domain.∙ f (x) = x5 + 1This is a bijection since the inverse function is f−1(x) =a)Let S = {−1, 0, 2, 4, 7}. Find f_image (S) if∙ f (x) = 1.f_image (S) = {1}∙ f (x) = 2x + 1.f_image (S) = {−1, 1, 5, 8, 15}∙ f (x) = ⌈x /5⌉.f_image (S) = {0, 1, 2}∙ f (x)=⌊(x2 + 1)/3⌋.f_image (S) = {0, 1, 5, 16}b) Find f ◦ g and g ◦ f , where f (x) = x2 + 1 and g(x) = x + 2, are functions from R to R.c) Let f (x) = ax + b and g(x) = cx + d, where a, b, c, and d are constants. Determine necessary and sufficient conditions on the constants a, b, c, and d so that f ◦ g = g ◦ f .d) Show that the function f (x) = ax + b from R to R is invertible, where a and b are constants, with a ≠ 0, and find the inverse of f .∙This function is a bijection when a≠0.o when f(y)=ay+b and f(z)=az+b → f(y)=f(z) ; ay+b=az+b → y=z f is one-to-oneo f is also onto since y=(x-b)/a for all y in R.∙f−1(x) = (x-b)/aa) Find the solution to each of these recurrence relations with the given initial conditions. Use an iterative approach.∙a n= −a n−1, a0 = 5∙a n = a n−1− n, a0 = 4a∙a n = 2a n−1− 3, a0= −1∙a n = 2na n−1, a0 = 3b)A person deposits $1000 in an account that yields 9% interest compounded annually.∙Set up a recurrence relation for the amount in the account at the end of n years.∙Find an explicit formula for the amount in the account at the end of n years.∙How much money will the account contain after 100 years?c) An employee joined a company in 2009 with a starting salary of $50,000. Every year this employee receives a raise of $1000 plus 5% of the salary of the previous year.∙Set up a recurrence relation for the salary of this employee n years after 2009.∙What will the salary of this employee be in 2017?∙Find an explicit formula for the salary of this employee n years after 2009.a)Determine whether each of these sets is countable or uncountable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set.∙integers not divisible by 3∙the real numbers with decimal representations consisting of all 1s∙the real numbers with decimal representations of all 1s or 9s∙This set is countable but a little tricky. We can arrange the numbers in a 2-dimensional table as follows:Thus we have shown that our set is the countable union of countable sets (each of the countable sets is one row of this table). Therefore, the entire set is countable. For an explicit correspondence with the positive integers, we can zigzag along the positive-sloping diagonals 1 ⟷ .1, 2 ⟷ 1.1,3 ⟷ .1,4 ⟷ .11,5 ⟷ 1, and so on.∙This set is not countable. We can prove it by the same diagonalization argument as was used to prove that the set of all reals is uncountable. All we need to do is choose d i = 1 when d ii = 9 andchoose d i = 9 when d ii = 1 or d ii is blank (if the decimal expansion is finite).b) Give an example of two uncountable sets A and B such that A − B is∙finite.∙countably infinite.∙uncountable.a) Determine whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) ∈ R if and only if∙x + y = 0.∙x = ±y.∙x = 2y.∙xy ≥ 0.b) For each of these relations on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive.∙{(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)}not reflexive ; not symmetric ; not antisymmetric ; transitive∙{(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4)}reflexive ; symmetric ; not antisymmetric ; transitive∙{(2, 4), (4, 2)}not reflexive ; symmetric ; not antisymmetric ; not transitive∙{(1, 2), (2, 3), (3, 4)}not reflexive ; not symmetric ; antisymmetric ; not transitivec) Write all binary relations on the set A={a,b}. Determine which ones are reflexive, symmetric, antisymmetric, transitive and/or functions from A to A.{} not reflexive ; symmetric ; antisymmetric ; transitive ; not function{(a,a)} not reflexive ; symmetric ; antisymmetric ; transitive ; not function{(a,b)} not reflexive ; not symmetric ; antisymmetric ; transitive ; not function{(b,a)} not reflexive ; not symmetric ; antisymmetric ; transitive ; not function{(b,b)} not reflexive ; symmetric ; antisymmetric ; transitive ; not function{(a,a),(a,b)} not reflexive ; not symmetric ; antisymmetric ; transitive ; not function{(a,a),(b,a)} not reflexive ; not symmetric ; antisymmetric ; transitive ; function{(a,a),(b,b)} reflexive ; symmetric ; antisymmetric ; transitive ; function{(a,b),(b,a)} not reflexive ; symmetric ; antisymmetric ; not transitive ; function{(a,b),(b,b)} not reflexive ; not symmetric ; antisymmetric ; transitive ; function{(b,a),(b,b)} not reflexive ; not symmetric ; antisymmetric ; transitive ; not function{(a,a),(a,b),(b,a)} not reflexive ; symmetric ; not antisymmetric ; not transitive ; not function {(a,a),(a,b),(b,b)} reflexive ; not symmetric ; antisymmetric ; transitive ; not function{(a,a),(b,a),(b,b)} reflexive ; not symmetric ; antisymmetric ; transitive ; not function{(a,b),(b,a),(b,b)} not reflexive ; symmetric ; antisymmetric ; not transitive ; not function{(a,a),(a,b),(b,a),(b,b)} reflexive ; symmetric ; not antisymmetric ; transitive ; not functiona) Suppose that R and S are reflexive relations on a set A. Prove or disprove each of these statements.∙R ∪ S is reflexive.∙R ∩ S is reflexive.∙S ◦ R is reflexive.b) Show the following properties on relations∙Show that the relation R on a set A is symmetric if and only if R = R−1, where R−1 is the inverse relation.Let (x,y) ∊ R(y,x) ∊ R since R is symmetric(x,y) and (y,x) ∊ R−1 by definition of inverse relationSo, R=R−1∙Show that the relation R on a set A is antisymmetric if and only if R ∩ R−1 is a subset of the diagonal relation Δ = {(a, a) | a ∈ A}.∙Show that the relation R on a set A is reflexive if and only if the inverse relation R−1 is reflexive.R is reflexive iff ∀x[x∊U ⟶ (x,x) ∊ R]iff ∀x[x∊U ⟶ (x,x) ∊ R-1] by definition of inverse relationR-1 is reflexivea)Which of these relations on the set of all people are equivalence relations? Determine the properties of an equivalence relation that the others lack.∙{(a, b) | a and b are the same age}equivalence relation∙{(a, b) | a and b have the same parents}equivalence relation∙{(a, b) | a and b share a common parent}This is not an equivalence relation, since it need not be transitive. (We assume that biologicalparentage is at issue here, so it is possible for A to be the child of W and X, B to be the child of X and Y, and C to be the child of Y and Z . Then A is related to B, and B is related to C, but A isnot related to C.)∙{(a, b) | a and b speak a common language}This is not an equivalence relation, since it need not be transitive.b)∙Show that the relation R consisting of all pairs (x, y) such that x and y are bit strings of length three or more that agree in their first three bits is an equivalence relation on the set of all bitstrings of length three or more.Transitive equivalence relation∙Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc. Show that R is an equivalence relation.Q10)a) Which of these relations on {0, 1, 2, 3} are partial orderings? Determine the properties of a partial ordering that the others lack.∙{(0, 0), (2, 2), (3, 3)}∙{(0, 0), (1, 1), (2, 0), (2, 2), (2, 3), (3, 3)}∙{(0, 0), (1, 1), (1, 2), (2, 2), (3, 1), (3, 3)}∙{(0, 0), (1, 1), (1, 2), (1, 3), (2, 0), (2, 2), (2, 3), (3, 0), (3, 3)}b)Let (S,R) be a poset. Show that (S,R−1) is also a poset, where R−1 is the inverse of R. The poset (S R−1) is called the dual of (S,R).。
function的用法和短语
function的用法和短语Function是函数的意思。
在编程语言中，函数是指一段可以被多次调用的代码块，通常接受参数并返回结果。
Function的用法：1.定义函数在编程语言中，定义函数通常需要指定函数名、参数列表和函数体。
例如，在JavaScript中定义一个函数可以这样写：```function add(a, b) {return a + b;}```2.调用函数调用函数时需要传递参数。
例如，在JavaScript中调用add函数可以这样写：```var result = add(1, 2);```3.匿名函数匿名函数是没有名称的函数，通常用于作为参数传递给其他函数。
例如，在JavaScript中可以这样定义一个匿名函数：```var add = function(a, b) {return a + b;}```4.高阶函数高阶函数是指接受一个或多个函数作为参数，或者返回一个函数作为结果的函数。
例如，在JavaScript中可以这样定义一个高阶函数：```function operate(a, b, fn) {return fn(a, b);}var result = operate(1, 2, add);```Function的短语：1. Function callFunction call是指调用函数的过程。
例如，在JavaScript中调用add函数可以称为一次Function call。
2. Function signatureFunction signature是指函数的参数列表和返回值类型。
例如，在Java中可以这样定义一个函数的Function signature：```int add(int a, int b);```3. Function pointerFunction pointer是指指向函数的指针。
例如，在C语言中可以这样定义一个函数指针：```int (*fp)(int, int);```4. Function overloadingFunction overloading是指在同一个作用域内定义多个函数名相同但参数列表不同的函数。
Homework_2
Homework_2一、名词解释（每小题3分，共15分）1.菌落2.培养基3.科赫法则4.逆转录病毒5.异形胞二、填空题（将答案写在答题纸的相应位置。
每空0.5分，共15分）1.成功进行曲颈瓶实验，彻底否定了“自然发生学说”的科学家是------。
2.原核微生物的细胞壁特有的组分是------，它是由------, ------和------组成的亚单位聚合而成。
酵母菌的细胞壁主要成分是------和------。
而大部分霉菌的细胞壁是由------组成的。
3.微生物的所需营养物质（五大要素）分别是------、------、------、------、------。
4.Woose提出的生物分类的三（原）界系统分别是------、------和------ 。
5.Bdellovibrio的主要特点是能在寄主细胞------之间生长繁殖，这是一种典型的微生物与微生物之间的------关系。
6.烈性噬菌体的增殖分为------、------、------、------ 和------五步。
7.真菌有性生殖过程分------、------ 和------三阶段。
8.对脂溶剂敏感的病毒一般具有------。
9.荚膜的主要化学成分有------、------等。
10.Mycoplasma菌落为典型的------。
三、选择题（1－12为单项选择。
13－15为多项选择。
每小题1分，共15分）1．Streptomyces的菌体呈分枝丝状体,因此它是一种_______。
A、多细胞的真核微生物B、单细胞的真核微生物C、多核的原核微生物D、无壁的原核微生物2．属于古菌的原核微生物是______。
A、HalobacterB、AcetobacterC、NitrobacterD、Azotobacter 3．微生物细胞中的a w值通常是。
A、细菌>酵母>霉菌>嗜盐菌B、酵母>霉菌>细菌>嗜盐菌C、霉菌>酵母>细菌>嗜盐菌D、嗜盐菌>霉菌>酵母>细菌4．细菌鞭毛运动所需的ATP来源于______。
计算机等级考试-二级C语言上机考试题库及答案
1.填空给定程序的功能是调用fun函数建立班级通讯录。
通讯录中记录每位学生的编号，姓名和电话号码。
班级的人数和学生的信息从键盘读入，每个人的信息作为一个数据块写到名为myfile5.dat的二进制文件中。
请在程序的下划线处填入正确的内容并把下划线删除，是程序得出正确的结果。
注意：源程序存放在考生文件夹下的BLANK1.c中不得增行或删行，也不得更改程序的结构！void check();/**********found**********/int fun(___1___ *std){/**********found**********/___2___ *fp; int i;if((fp=fopen("myfile5.dat","wb"))==NULL)return(0);printf("\nOutput data to file !\n");for(i=0; i<N; i++)/**********found**********/fwrite(&std[i], sizeof(STYPE), 1, ___3___);fclose(fp);return (1);}修改给定程序MODI1.C中函数fun的功能是：先将在字符串s中的字符按正序存放到t串中，然后把s中的字符按逆序连接到t串后面。
例如：当s中的字符串为：“ABCDE”时，则他中的字符串应为：“ABCDEEDCBA”。
请改正程序中的错误，使他能得出正确的结果。
注意：不要改动main函数，不能增行或删行，也不得更改程序的结构！void fun (char *s, char *t){ int i, sl;sl = strlen(s);/************found************/for( i=0; i<=s1; i ++)t[i] = s[i];for (i=0; i<sl; i++)t[sl+i] = s[sl-i-1];/************found************/t[sl] = '\0';}程序函数fun的功能是：将两个两位数的正整数a，b合并成一个整数放在c中。
小学下册T卷英语第六单元测验试卷
小学下册英语第六单元测验试卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.I like to _______ (和朋友一起)去旅行.2.What is the main function of a heart?A. Pump bloodB. Digest foodC. Filter wasteD. Store energyA3.We have _____ (春天) flowers blooming.4.The __________ was a time of significant social change in the 1960s. (社会运动)5.The Rosetta Stone helped scholars understand ________ language.6.My favorite hobby is ______ (gardening).7. A reaction that releases gas is called a ______ reaction.8.I need to _____ (finish/start) my homework.9.Which of these is NOT a planet?A. MarsB. EarthC. SunD. JupiterC10.The Titanic was a famous _______ ship.11.This is my best ___. (friend)12.What is the name of the mineral used to make salt?A. CalciumB. SodiumC. PotassiumD. Magnesium13.What is the name of the famous ancient city in Israel?A. JerusalemB. Tel AvivC. HaifaD. NazarethA Jerusalem14.The _____ (植物维护) requires knowledge and dedication.15.What do you call the process of providing nutrients to plants?A. FertilizationB. IrrigationC. CultivationD. Planting16.I want to _____ (become) a scientist.17.What do we call the process of capturing sunlight to produce energy?A. Solar EnergyB. Wind EnergyC. Hydroelectric EnergyD. Biomass EnergyA18.My favorite ________ is orange.19. A rock cycle describes how rocks change from one type to ______.20.What is the name of the famous scientist known for his work on the nature of light?A. Isaac NewtonB. Albert EinsteinC. James Clerk MaxwellD. Thomas YoungA21.What do we call the act of putting two or more numbers together?A. SubtractionB. DivisionC. AdditionD. MultiplicationC22.What do we call the layer of gases surrounding Earth?A. AtmosphereB. LithosphereC. HydrosphereD. BiosphereA23.The ancient Greeks held _____ to celebrate their achievements.24.The bear is a powerful animal, respected and feared in the wild ____.25.We have ______ (很多) books at home.26. A __________ is a chemical substance made of two or more different atoms bonded together.27.I build things with my ________ (玩具名称).28. A ____(climate zone) differs based on temperature and rainfall.29.Deltas are often home to diverse ______ species.30.I enjoy ______ (drawing) pictures.31.My friend is _______ (很有趣).32.What do we call the act of creating something new?A. InnovationB. InventionC. CreationD. DesignB33.What is the color of an avocado?A. YellowB. GreenC. BlueD. RedB34.What is the opposite of happy?A. SadB. AngryC. ExcitedD. Joyful35.We can _______ (一起) plant flowers.36.My brother is passionate about ____ (photography).37.How many zeros are in one thousand?A. TwoB. ThreeC. FourD. FiveB38. A parrot can ________________ (说话).39.My grandmother shares __________ (智慧) with us often.40. A ________ (火山口) is the opening of a volcano.41.I think being a __________ (志愿者) is very important.42.It is _____ (hot/cold) in winter.43.He is my best ________.44.What is the name of the famous river in Egypt?A. NileB. AmazonC. MississippiD. Yangtze45.I share my lunch with my __________. (朋友)46.We analyze ________ (results) for improvement.47.I like to _______ (paint) with watercolors.48. A ______ is a systematic method for collecting data.49.The life cycle of a flower includes growth, blooming, and ______. (花的生命周期包括生长、开花和凋谢。
Homework 2
Homework 2: 英译汉、汉译英1.省译法1）We expect that the delivery will be effected at your earliest convenience.2）It’s a pleasure for us to offer you the goods as follows.3）To give you a general idea of the various kinds of cotton piece goods now available for export, we enclose a brochure and a price list.2.增译法1）Inflation was and still is the No. 1 problem of that country.2）Courage in excess becomes foolhardiness, affection weakness, thrift avarice.3.词性转换法1）企业组织可以选择在报纸或杂志上登广告，简要介绍所招聘职位的情况并征集应聘者的自荐信。
（动词翻译成名词）2）If major problems exist and goals are not being achieved, then changes need to be made in the company’s organizational or managerial structure. （名词翻译成动词）3）We are especially grateful to you for arranging the meeting for us with the Machinery Trading Delegation at such short notice. （形容词翻译成动词）4.被动语态1）The damage was covered by the insurance company.2）The Chinese trade delegation was given a hearty welcome.3）He preferred to be assigned something concerning trade to do.4）英文版学校简介运用形容词来代替名词。
外研社英语必修二教案
外研社英语必修二教案外研社英语必修二教案【篇一：外研社必修2英语优秀教案】1. lesson plan1.1 background informationjunior or senior sectionteachersize class , gradetime type of lessonteaching1.2 contents vocabulary:words that need to be recognize: court, director, genius, harpsichord, impressed,lose, musical, peasant, piece of music, singer,successful, symphony, talent, teenager.reading: three great composers of the eighteenth century1.3 objectivesby the end of the class, students should be able to:1.3.1 instructional objectives1) recognize and know the pronunciations and meanings ofthe following vocabularies by showing pictures, situations, word-formation rules, chunks, collocation, teacher’s explaini ng and guessing though the context:court, director, genius, harpsichord, impressed, lose, musical, peasant, piece of music, singer,successful, symphony, talent, teenager.2) grasp the key words, understand the main idea of the reading materials ;3.3.2 educational objectives1) strengthen their motivation and interest in learning english through the interesting class activities;2) build up the cooperative spirit by pair working and groupworking;3) talk about some famous composers;4) use the cognitive strategies to learn new words.3.3.3 personal objectivesteacher tries to be more passionate and involved all students in my class.3.4 focal points1) students are able to use the reading skills to grasp the key words, organize information by tables.2) students are able to write a short passage to introduce their favorite musicians.3.5 difficult pointsstudents are able to use the reading skills to gain information and compare the information.3.6 procedures and time allotment3.6.1 getting students ready for learning (3 minutes)step 1 greetingsteacher greets students with simple communication.t: good morning, boys and girls. how are you today?ss: …t: shall we begin our class?ss: yes.3.6.2 revision (2minutes)review what we have learned yesterday.3.6.3 pre-reading (6 minutes)step 1 enjoy a piece of music by beethoven on ppt.step 2 vocabulary presentationteacher shows some pictures about the three great composers of the eighteenth century; at the same time, students learn some new words:court, director, genius, harpsichord,impressed, lose, musical, peasant, piece of music, singer, successful, symphony, talent, teenager.teacher pays some attention to students’ pronunciation. then teacher leads students to the text by asking questions.3.6.4 while-reading (20 minutes)step1 skimming the passage for the main idearead the passage quickly and choose the best title in ex2 on p22---three great austrian composers---three great composers of the eighteenth century---three great child composersstep 2 scanning the passage for specific information read the passage again and answer the questions. which of the composers....1. were born in austria?2. was born in germany?3. had a good singing voice?4. died before his fortieth birthday?5. became deaf?6. met each other?7. had fathers who were musicians?8. had a father who wasn’t a musician?step3 read the passage carefully and fill in the form.about haydn【篇二：外研社高一英语必修二 module 2 教案】 lesson plan practice teacher’s name: ren baiyunteaching date: nov. 28, 2012【篇三：外研版高中英语必修2---module4教案】module fourfine arts-western,chinese and pop artsperiod oneteaching content:introduction; reading and vocabularyteaching important points:1.encourage the students to talk about arts as well as the well-known artists at home and abroad;2.help the students make sense of the whole passage;3.help the students improve their reading ability.teaching difficult points:1.lead the students to talk in class actively;2.deal with some difficult language points.teaching procedures:step 1 lead-in and introduction1.lead-ini think most of us love different kinds of arts and know about some famous artists and famous art works more or less.now let`s list some famous artists and their famous art works at home and abroad,such as:qi baishi and his painting of shrimps,xu beihong and his painting of horses,zheng banqiao and his works of bamboos at home.abroad there are da vinci and his the smile of mona lisa,vincent van gogh and his the sunflowers（《向日葵》）and the starry night（《星夜》）,pablo picasso and cubism(立体主义画派) and so on.this module we`ll talk about the topic-fine arts.first let`s review some words related to it.2.activity1 on p31ask the students to read through the questions and words in this part to understand;explain some of the words if necessary and then ask the students to read out them aloudtogether;if possible ask some students to give their answers to the questions(if not,the questions can be omitted.).3.activity2 on p31read through the given information to understand the requirement and appreciate the paintings by themselves.if possible ask some students to present their answers to the class.[there are no standard answers.students` own answers are ok.] step 2 pre-reading[activity1 on p32]read through the given information to understand and try to match;explain some words if necessary and then ask the class to read out the words together aloud;call back the answers from the students.step 3 reading1.fast readinglet the students scan the passage to get the main idea of each paragraph and try to find out the answers to the questions in activity2 on p32, which are about the topics.the first four paragraphs describe the four paintings and in the last two paragraphs two students talk about their opinions about two of the paintings.then call back the answers./doc/7d7236780.html,nguage points[ref:notes to the text]explain some language points to the students.3.careful readingask the students to read through the passage again carefully to get more details and understand it better.then finish activity3 on p34.call back the answers.step 4 consolidationtime permitting,let the students listen to the tape and follow it quietly to understand the text further.step 5 summary and homework1.summary: summarize what they have learned in this period.2.homework: reading on p88-89 in workbook.appendix: notes to the text1.?that aimed to show ordinary twentieth-century city life.aim to do sth. 打算做某事，目的是[aim vi. 打算]eg:they are aiming to reduce unemployment by 50%.we aim to be there around six.我们力争六点钟左右到那里。
Homework Exercise 2
Homework Exercise 2: Team LeadershipName: Yishu WangStudent ID: z5005638(a)Briefly describe the project’s background, i.e. context and purpose.I would like to describe a leadership experience when I was doing the project of ‘The Expansion of the S miths’ Lake Field S tation’. The m ain purpose of this project is to provide some potential favourable areas for the expansion of Smiths Lake Field Station. This project includes analysis and evaluation of all the sites based on several criteria(minimal construction cost, low probability in any natural disaster, not affect any conservation area). Through weighting to each criterion, the factor of ‘suitability to build’ had been selectedas the first priority. Surface visibility and solar radiation are the additional factors that assist in the ranking of the sites selections.(b)Explain how design choice and other engineering decisions were madeduring completion of this project.The structure design was the most time–consuming problem that we faced during the whole process. To be specific, this core part of the project determined how each model correlated with others and how can we combined them all and give certain weightings to obtain the final output.At the first stage, out team met for several times and discussed about the proper structure for our evaluating mechanism, and gradually it turned out to be a clue for implementation. Generally, whenever we were going to make decisions, divergence may remain at the first. Theneveryone in our team would express their standpoints and the reason why they persist in his or her view. Finally, we may vote for the finaldecision if we still could not reach a consensus.We also find that consulting some of the professional seniors in our field is a very wise idea.Havingmore good communications with our team, and looking for related materials as effective as possible can also help us a lot when engineering decisions were to be made.(c)Discuss the feat ure of the leadership shown in your project’s team.Considering the idea discussed in this course, do you think it was generally “effective”? Did it display“excellence”? Explain your answer.Leadership playssignificantly important role in our project. Without a certain leader or representative, we could not work as effective as we did. It is intuitive to find that people who are extravert, charismatic and have decent communication skills are competent to be a leader for a team. For most of the cases, every team faces controversy or approaching deadlines which could easily make members frustrated and anxious, however we find that most of our leaders are able to inspire the team at right time and appropriate way to enhance the efficiency.On the other hand, leaders show their talent in every way. I should say that the effective leadership is to some extent based on a good knowledge. They got the management skill but what they do is more than control and organizing of the team. They are visionary andpersistent and can set clear goals for every step of the team work. As most of the time leaders are seniors in this professional field which have a strong background to back them up, they actas helpers to support both technologically and spiritually.What is more, they are charismatic and could attract people’s attention in every meeting or daily conversation, potentially cre ate trust from the subordinate and easily influence the team member’s a ttitude on work. Besides, Leaders can make the team member feel they are respected, and theirworks are recognised by the leader which contribute to build up a friendly workplace and also enhance the efficiency.。
Homework2
Solution of Homework 2Dragon:4.2.1, 4.2.4, 4.2.5, 4.2.74.3.14.4.3Tiger:3.4, 3.5, 3.6, 3.7Dragon Book4.2.1 Considering the context-free grammar:and the string aa+a*(1)Give a leftmost derivation of the string(2)Give a rightmost derivation of the string(3)Give a parse tree for the string(4)Is the grammar ambiguous?(5)Describe the language generated by the grammar答案：(1)(2)(3)SSS* S S+a aa(4)没有二义性(5)只含+和*，操作数均为a的算术表达式的后序遍历4.2.4 Show that [] and {} extension do not add power to grammars.答案: S->[a] 等价于S->S->{a} 等价于S->S’S’ -> ’4.2.5 Use notations from 4.2.4 to simplify the following grammar:答案：stmt-> if expr then stmt [else stmt]| begin stmtList endstmtList -> stmt{;stmt}4.2.7 A grammar symbol X (terminal or non-terminal) is useless if there is no derivation of the form . That is, X can neverappear in the derivation of any sentence.(1) Give an algorithm to eliminate all productions contains useless symbols(2) Apply your algorithm to grammar:S-> 0 | AA-> ABB->1答案：(1)注意：首先要考虑产生式是否终止，其次考虑是否在产生式中出现(a)求出非终结符是否终止对于每个非终结符X若X存在产生式不含非终结符，则X终止否则，对于X的每个产生式中的非终结符，若含有X，则X不终止，否则，若每个非终结符均终止，则X终止，否则不终止(b)去掉useless令文法G为空从起始的非终结符X开始对于X的每个产生式P，若P不含非终结符，则将X->P加入文法G否则，若P中每个非终结符均终止，则将X->P加入文法S’，并对每个非终结符X’递归调用这个过程返回文法G算法并不唯一，这只是一个很罗嗦的实现(2)对于这里给出的算法首先S和B终止，A不终止然后从S->0开始，S->0加入文法GS->A,A不终止，至此递归调用结束所以最终返回结果S->04.3.1 The following grammar for regular expressions over symbols a andb only.(1)Left factor this grammar(2)Does left factoring make the grammar suitable for top-down parsing?(3)Eliminate left recursion from the original grammar(4)Is the resulting grammar suitable for top-down parsing?答案：(1)rexpr -> rexpr + rterm | rtermrterm -> rterm rfactor | refactorrfactor -> rfactor * | rprimaryrprimary-> a| b(2)不可以，因为存在左递归(3)rexpr -> rterm rexpr’rexpr’-> + rterm rexpr’ |rterm-> rfactor rterm’rterm’ -> rfactor rterm’ |rfactor-> rprimay rfactor’rfactor’-> *rfactor’ |rprimary-> a | b(4)可以4.4.3 计算练习4.2.1中文法的FIRST和FOLLOW集合答案：FIRST(S)=aFOLLOW(S)= $a+*Tiger Book3.4 Write a grammar that accepts the same language as Grammar 3.1, but that us suitable for LL(1) parsing. That is, eliminate the ambiguity, eliminate the left recursion, and (if necessary) left-factor.Grammar 3.1:S -> S; SS -> id := ES -> print ( L )E -> idE -> numE -> E + EE -> ( S , E )L -> EL -> L , EAnswer:S -> id := E ; SS -> print ( L ) ; SE -> ( S , E )E -> id E’E -> num E’E’ -> εE’ -> + EL -> E L’L’ ->εL’ -> , E L’3.5 Find nullable, FIRST, and FOLLOW sets for the grammar; then construct the LL(1) parsing table.S’ -> S $S ->S -> X SB -> \ begin { WORD }E -> \ end { WORD }X -> B S EX -> { S }X -> WORDX -> beginX -> endX -> \ WORDAnswer:3.6a. Calculate nullable, FIRST, and FOLLOW for this grammar:S -> u B D zB -> B vB -> wD ->E FE -> yE ->F -> xF->b. Constructor the LL(1) parsing table.c. Give evidence that this grammar is not LL(1).d. Modify the grammar as little as possible to make an LL(1) grammar that accepts the same language.Answer:a)c) b中构建的LL(1)转换表中含有包含多个语法规则的表项，所以该语法不是LL(1)语法。
Homework2
= m1 d, n = n1 d, where d = (m, n). We claim that o(ab) = m1 n1 d. m n d Indeed, (ab) =a b = (am )n (bn )m = 1, so o(ab)|m1 n1 d. sm Set s = o(ab). Since 1 = (ab) = a sm b sm = b sm and 1 = (ab) sn = a sn b sn = a sn , so n| sm and m| sn hold. Then n1 | sm1 and m1 | sn1 together imply that n1 | s and m1 | s since (m1 , n1 ) = 1. Furthermore, m1 n1 | s. Thus, o(ab) = km1 n1 for some positive integer k, k|d . In particular, if (m, n) = 1, then o(ab) = mn.
→
G
2
6. Let W be the additive subgroup of linear equations AX form a coset of W .
Rm
of solutions of a system of homogeneous
=
0. Show that the solutions of an inhomogeneous system AX
1
9. Consider the set U of real 3
(a) Prove that U is a subgroup of S Ln (R). (b) Prove or disprove: U is normal. (c) Determine the center of U . Proof (a) It is easily veri ed that U is closed with respect to the multiplication of matrices. Moreover, the identity I3 is in U , and the inverse matrix of every element of U is its adjoint matrix, which is also contained in U . So U is a subgroup of S Ln (R). (b) U isn't a normal subgroup of S Ln (R). For example, choose
小学上册L卷英语第二单元测验卷
小学上册英语第二单元测验卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.I _____ (love/hate) homework.2.The _____ (车站) is busy.3.The study of how landscapes evolve can provide insights into ______ change.posting can provide ______ (天然肥料) for gardens.5. A star's brightness is measured in ______.6.What do you call a large area of water surrounded by land?A. OceanB. SeaC. LakeD. RiverC7.The sun rises in the ______ (east).8.What do we call the study of human societies?A. SociologyB. AnthropologyC. PsychologyD. Political ScienceA9.I love to write ______ (故事) about my adventures and experiences.10.The _____ (fireworks) are colorful.11.What do we call the study of the Earth's atmosphere and weather?A. GeologyB. MeteorologyC. ClimatologyD. OceanographyB12.How many legs does an insect have?A. SixB. EightC. FourD. TenA13.What is the name of the fairy in Peter Pan?A. TinkerbellB. CinderellaC. ArielD. Snow WhiteA14.The donkey is often _______ (驮) heavy loads.15.What is the largest desert in the world?A. SaharaB. GobiC. ArabianD. AntarcticD Antarctic16.The _____ (车站) is nearby.17.The chemical symbol for tin is _____.18.What do you need to write on a board?A. PenB. MarkerC. PencilD. Paint19.The __________ is a large desert in Australia.20.The owl can rotate its head almost ______ (完全) around.21. A __________ is a large area of land that has a specific climate and vegetation. (气候区)22.What is the sound a duck makes?A. QuackB. MooC. BaaD. RoarA23.I like to play with my ________ in the sand.24.小猫) loves to chase after strings. The ___25.The ancient Sumerians are credited with creating the first _____.26. A pure substance cannot be separated into simpler _____ (substances) by physical means.27.The owl has big _________. (眼睛)28.What is the name of the first successful Mars rover mission?A. SpiritB. OpportunityC. CuriosityD. Perseverance29.The ________ is a friendly creature that loves to cuddle.30. A solution can become saturated when it holds the maximum amount of ______.31.中国的________ (artifacts) 让我们了解过去的文明。
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Write the code to solve these problems:
Structured Programming
1.Write a program include a function to find the number which can be divided by 3
and also can be divided by 7 in the range 100 to 1000. Write the function to make the decision and apply it in main function from 100 to 1000.
2.Write a program: input a integer from keyboard, write a function to calculate the
sum of the digits on every bits of this number. For example: input 1234, the sum is 1+2+3+4. Output the sum on the screen.
Arrays:
3.Create a program that will search a numeric value in an array. If a match is found,
print the index number of that element and exit the loop. If no match was found, alert the user with “Sorry, your search value was not found”
4.Create a program that will store the integers 8–12 (including 8 and 12) into an
array and output the mount of the even integers.
Structured Programming & Arrays:
4.Create a function that will output the odd integers of an array. The array has 6
elements, and is inputted in the main( ) by the user.
#include<stdio.h>
void iodd (int a[])
{ int i;
for(i=0;i<=5;i++)
{
if(a[i]%2!=0)
printf("%d is a odd\n",a[i]);
}
}
main()
{
int a[6];
int i;
clrscr();
for(i=0;i<=5;i++)
{
printf("please input a number:");
scanf("%d",&a[i]);
}
iodd(a);
return 0; }。