大学数学,专业英语课后答案
高一英语大学专业选择单选题50题
高一英语大学专业选择单选题50题1. Which of the following is a major related to computer science?A. PsychologyB. EngineeringC. LiteratureD. Biology答案：B。
本题考查对大学专业名词的理解。
选项A“Psychology”是心理学；选项C“Literature”是文学；选项D“Biology”是生物学。
而选项B“Engineering”工程学与计算机科学相关，所以选B。
2. If you are interested in medicine, which major should you choose?A. PhysicsB. ChemistryC. HistoryD. Art答案：B。
本题考查与医学相关的专业。
选项A“Physics”是物理学；选项C“History”是历史学；选项D“Art”是艺术。
化学与医学密切相关，所以应选B“Chemistry”。
3. Which major is focused on the study of human behavior and mental processes?A. SociologyB. AnthropologyC. PsychologyD. Geography答案：C。
此题考查对不同专业研究内容的了解。
选项A“Sociology”是社会学；选项B“Anthropology”是人类学；选项D“Geography”是地理学。
而“Psychology”心理学是研究人类行为和心理过程的专业，故选C。
4. For those who want to design buildings, which major is suitable?A. ArchitectureB. MusicC. PhilosophyD. Math答案：A。
本题关于建筑设计相关专业。
2024考研(数学三)真题答案及解析完整版
2024考研(数学三)真题答案及解析完整版2024年全国硕士研究生入学考试数学(三)真题及参考答案考研数学三考什么内容?数学三在高等数学这一部分因为要求的内容相对较少，所以很多学校经济类、管理类专业在本科期间所用教材并非理工类专业通常会使用的《高等数学》同济大学版，更多的学校本科阶段的教材是中国人民大学版《微积分》。
而考数学三的同学中在实际复习过程中使用哪一本教材的都有)(函数、极限、连续、一元函数微分学、一元函数积分学、多元函数微积分学、无穷级数、常微分方程与差分方程);线性代数(行列式、矩阵、向量、线性方程组、矩阵的特征值和特征向量、二次型);概率论与数理统计(随机事件和概率、随机变量及其分布、多维随机变量及其分布、随机变量的数字特征、大数定律和中心极限定理、数理统计的基本概念、参数估计、假设检验)。
考研的考试内容有哪些一、考研公共课：政治、英语一、英语二、俄语、日语、数学一、数学二、数学三，考研公共课由国家教育部统一命题。
各科的考试时间均为3小时。
考研的政治理论课(马原22分、毛中特30分、史纲14分、思修18分、形势与政策16分)。
考研的英语满分各为100分(完型10分、阅读理解60分、小作文10分、大作文20分)。
数学(其中理工科考数一、工科考数二、经管类考数三)满分为150分。
数一的考试内容分布：高数56%(84分)、线代22%(33分)、概率22%(33分);数二的内容分布：高数78%(117分)、线代22%(33分);数三的内容分布：高数56%(84分)、线代22%(33分)、概率22%(33分)。
这些科目的考试知识点和考试范围在各科考试大纲上有详细规定，一般变动不大，因此可以参照前一年的大纲，对一些变动较大的科目，必须以新大纲为准进行复习。
二、考研专业课统考专业课：由国家教育部考试中心统一命题，科目包括：西医综合、中医综合、计算机、法硕、历史学、心理学、教育学、农学。
其中报考教育学、历史学、医学门类者，考专业基础综合(满分为300分);报考农学门类者，考农学门类公共基础(满分150分)。
高一英语大学专业选择因素单选题50题(带答案)
高一英语大学专业选择因素单选题50题(带答案)1.Which of the following is the most important factor when choosinga college major according to your interests?A.Good job prospectsB.High salaryC.Personal interestD.Famous university答案：C。
解析：根据兴趣选择大学专业时，个人兴趣是最重要的因素。
选项A“良好的就业前景”、选项B“高薪水”和选项D“著名大学”虽然也很重要，但如果没有个人兴趣作为支撑，可能会在学习过程中感到枯燥和困难。
2.If you are interested in art, which college major is the most suitable for you?puter ScienceB.English LiteratureC.Fine ArtsD.Mathematics答案：C。
解析：如果对艺术感兴趣，美术专业是最适合的。
选项A“计算机科学”、选项B“英语文学”和选项D“数学”与艺术的相关性较小。
3.Your hobby is playing musical instruments. Which major might you be interested in?A.MusicB.PhysicsC.BiologyD.History答案：A。
解析：爱好是演奏乐器，那么音乐专业可能会感兴趣。
选项B“物理”、选项C“生物”和选项D“历史”与乐器演奏的关联性不大。
4.You love reading novels. Which college major could be a good choice?A.LiteratureB.ChemistryC.EngineeringD.Accounting答案：A。
第3版新视野大学英语4读写教程课后练习题答案(1-6单元)
Unit 1Words in use1.As the gender barriers crumbled, the number of women working as lawyers, doctors, or bankers began to increase significantly from the mid-20th century.随着性别壁垒的瓦解, 从20世纪中期开始, 从事律师、医生或银行家工作的妇女人数开始显著增加。
2.With the data collected each year, the owner of the shop can discern customer trends and how things like weather and economic indicators affect sales performance.通过每年收集的数据, 店主可以辨别顾客的趋势, 以及天气和经济指标如何影响销售业绩。
3.His supervisor pushes and motivates him in such a positive manner that he is not only able to reach but to surpass his personal goals.他的上司以一种积极的方式推动和激励他, 使他不仅能够达到, 而且能够超越他的个人目标。
4.He is a man with a(n) shrewd business sense.He has built his initial investment intoa substantial and even excessively large fortune.他是个有精明商业头脑的人。
他把最初的投资变成了一笔可观的、甚至过多的财富。
5.The conversion of nuclear radiation directly into electricity was an exciting possibility that was being vigorously explored in many laboratories in the 1950s.核辐射直接转化为电能是一种令人兴奋的可能性, 20世纪50年代, 许多实验室正在积极探索这种可能性。
新编大学英语4(第二版)Unit 1-Unit 6单元 课文翻译及课后答案详解
课内阅读参考译文及课后习题答案(Book 4)Unit 1享受幽默—什么东西令人开怀？1 听了一个有趣的故事会发笑、很开心，古今中外都一样。
这一现象或许同语言本身一样悠久。
那么，到底是什么东西会使一个故事或笑话让人感到滑稽可笑的呢？2 我是第一次辨识出幽默便喜欢上它的人，因此我曾试图跟学生议论和探讨幽默。
这些学生文化差异很大，有来自拉丁美洲的，也有来自中国的。
我还认真地思考过一些滑稽有趣的故事。
这么做完全是出于自己的喜好。
3 为什么听我讲完一个笑话后，班上有些学生会笑得前仰后合，而其他学生看上去就像刚听我读了天气预报一样呢？显然，有些人对幽默比别人更敏感。
而且，我们也发现有的人很善于讲笑话，而有的人要想说一点有趣的事却要费好大的劲。
我们都听人说过这样的话：―我喜欢笑话，但我讲不好，也总是记不住。
‖有些人比别人更有幽默感，就像有些人更具有音乐、数学之类的才能一样。
一个真正风趣的人在任何场合都有笑话可讲，而且讲了一个笑话，就会从他记忆里引出一连串的笑话。
一个缺乏幽默感的人不可能成为一群人中最受欢迎的人。
一个真正有幽默感的人不仅受人喜爱，而且在任何聚会上也往往是人们注意的焦点。
这么说是有道理的。
4 甚至有些动物也具有幽默感。
我岳母从前经常来我们家，并能住上很长一段时间。
通常她不喜欢狗，但却很喜欢布利茨恩—我们养过的一条拉布拉多母猎犬。
而且，她们的这种喜欢是相互的。
布利茨恩在很小的时候就常常戏弄外祖母，当外祖母坐在起居室里她最喜欢的那张舒适的椅子上时，布利茨恩就故意把她卧室里的一只拖鞋叼到起居室，并在外祖母刚好够不到的地方蹦来跳去，一直逗到外祖母忍不住站起来去拿那只拖鞋。
外祖母从椅子上一起来，布利茨恩就迅速跳上那椅子，从它那闪亮的棕色眼睛里掠过一丝拉布拉多式的微笑，无疑是在说：―啊哈，你又上了我的当。
‖5 典型的笑话或幽默故事由明显的三部分构成。
第一部分是铺垫（即背景），接下来是主干部分（即故事情节），随后便是妙语（即一个出人意料或令人惊讶的结尾）。
数学专业英语课后答案
2.1数学、方程与比例词组翻译1.数学分支branches of mathematics，算数arithmetics，几何学geometry，代数学algebra，三角学trigonometry，高等数学higher mathematics，初等数学elementary mathematics，高等代数higher algebra，数学分析mathematical analysis，函数论function theory，微分方程differential equation2.命题proposition，公理axiom，公设postulate，定义definition，定理theorem，引理lemma，推论deduction3.形form，数number，数字numeral，数值numerical value，图形figure，公式formula，符号notation(symbol)，记法/记号sign，图表chart4.概念conception，相等equality，成立/真true，不成立/不真untrue，等式equation，恒等式identity，条件等式equation of condition，项/术语term，集set，函数function，常数constant，方程equation，线性方程linear equation，二次方程quadratic equation5.运算operation，加法addition，减法subtraction，乘法multiplication，除法division，证明proof，推理deduction，逻辑推理logical deduction6.测量土地to measure land，推导定理to deduce theorems，指定的运算indicated operation，获得结论to obtain the conclusions，占据中心地位to occupy the centric place汉译英（1）数学来源于人类的社会实践，包括工农业的劳动，商业、军事和科学技术研究等活动。
江苏大学课后答案考试试题全免费下载
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高一英语大学专业选择指导练习题40题
高一英语大学专业选择指导练习题40题1. Which major is related to the study of living organisms?A. Computer ScienceB. BiologyC. MathematicsD. History答案解析：B。
Biology 是生物学，主要研究生物，与living organisms（生物体）相关。
Computer Science 是计算机科学，与生物体无关。
Mathematics 是数学，也不涉及生物体研究。
History 是历史，同样与生物体没有关系。
2. Which major focuses on the design and development of software?A. PhysicsB. ChemistryC. EngineeringD. Computer Science答案解析：D。
Computer Science 是计算机科学，专注于软件的设计和开发。
Physics 是物理学，与软件设计无关。
Chemistry 是化学，也不涉及软件。
Engineering 是工程学，范围比较广，但不是专门针对软件设计和开发。
3. Which major is concerned with the study of human behavior and mental processes?A. PsychologyB. EconomicsC. SociologyD. Literature答案解析：A。
Psychology 是心理学，研究人类行为和心理过程。
Economics 是经济学，主要研究经济现象。
Sociology 是社会学，关注社会现象。
Literature 是文学，与人类行为和心理过程的研究关系不大。
4. Which major deals with the management of financial resources?A. AccountingB. MarketingC. PhilosophyD. Art答案解析：A。
高一英语大学专业选择因素单选题50题
高一英语大学专业选择因素单选题50题1. If your interest is in music, which major is the most suitable for you?A. Computer ScienceB. Music EducationC. EngineeringD. Business Administration答案：B。
本题考查对不同专业与兴趣的匹配。
选项A“Computer Science”主要涉及计算机领域，与音乐兴趣无关。
选项C“Engineering”侧重于工程方面，也与音乐兴趣不直接相关。
选项D“Business Administration”是商业管理，和音乐兴趣联系不大。
而选项B“Music Education”与音乐兴趣直接相关，是针对对音乐有兴趣的人的合适专业。
2. When your passion lies in art, which of the following majors should you consider?A. MedicineB. LawC. Fine ArtsD. Physics答案：C。
本题考查专业与兴趣的对应。
选项A“Medicine”是医学专业，与艺术兴趣不相符。
选项B“Law”是法律专业，和艺术兴趣没有直接关联。
选项D“Physics”是物理学专业，不属于艺术范畴。
而选项C“Fine Arts”是美术专业，与对艺术的兴趣高度契合。
3. If you are interested in sports, which major might be a good choice for you?A. LiteratureB. Physical EducationC. ChemistryD. History答案：B。
本题考查兴趣与专业的适配性。
选项A“Literature”是文学专业，与体育兴趣关系不大。
选项C“Chemistry”是化学专业，和体育兴趣没有直接联系。
新编大学英语2视听说Unit5答案+原文
Unit FivePart 1 Listening, Understanding and SpeakingListening IKeysExercise 1√1, √4, √5, √6, √7, √8Exercise 2ACDBExercise 31) strange, 2) strange force, 3) very steep, 4) at the bottom, 5) watching6) be punished, 7) in the darkness, 8)scared, 9)avoid ,10)exam,11) interpreting dreams, 12) disappointing, 13) making mistakes, 14) symbol Exercise 4Sample1. I think Jennifer’s nightmare has something to do with her fear of failure, failure in exams, failure in living up to her Parents’expectations etc. She probably didn’t do well at collage and she had experienced failures. What she feared in life was represented in her dream.2. I often have nightmares and my nightmares are generally the same. One typical nightmare I have is that I am chased by someone and I try to run fast but I can’t. And usually when I am about to be caught I wake up, sometimes sweating all over. I’ve told people about it and the interpretation given is that my schedule is too tight most of the time. I don’t know how Freud would interpret it, but the interpretation seems to make sense.ScriptPart AJennifer is talking to an interviewer about her nightmare.Jennifer: It was always the same. Always. I was in a house, a strange house, and I knew somehow that I shouldn’t have gone in. But there was some strange force pulling me. There were some stairs…very steep stairs… and I started to climb them, and … and then, suddenly fell. Then when I was at the bottom of the stairs, I suddenly realized that there was someone…or something else in the house with me, and that these eyes had been watching me all the time, and…I knew then that something terrible…was going to happen to me…that I was going to be punished…because I’d done something I shouldn’t have done. I didn’t know what it was, but I knew it was wrong, very wrong. Then I could hear it…whatever it was in the house withme…coming closer in the darkness, because everything was dark, you see, and it came closer and closer. And I was scared…and there was nothing, nothing I could do to avoid it…nothing. I was trapped! Trapped in that dark house at the bottom of the stairs. There was no way out.Interviewer: And how often…Jennifer: No way out !Part BInterviewer: How often have you had this nightmare?Jennifer: When I was in college, just about every time I had an exam. And then, a few years later, when I was taking an intensive Italian course in Italy, I had the same dream again. Just the same as before.Interviewer: And you discussed it with a psychoanalyst ?Jennifer: Yes, later, after I came back to Los Angles, I started therapy, and this dream came up, and we discussed it quite a bit.Interviewer: And what did the psychoanalyst say?Jennifer: He said…uh…you have to be very careful about interpreting dreams, but we both agreed that the dream was a symbol of my fear of failure…of disappointing my parents when I was in college, for example, by failing my dreams, or…or when I was taking that Italian course, I remember how scared I was sometimes.Interviewer: Scared of what?Jennifer: Of making mistakes in class, in front of the teacher or the other students. I was always in fear.Interviewer: I see.Jennifer: And the dream was a kind of classic symbol of that fear…of the fear of failure. Falling down stairs in a dream is a symbol of that. The two words are very similar.Interviewer: Which…which two words? Oh, you mean…Jennifer: Yes, fall-fail, falling-failure. Very similar, aren’t they?Listening IIKeysExercise 11.C2. A3. I4. H5. F6. D7. J8. GExercise 21.Because dreams are closely related to wakng lives.2.more women have careers.3.The possible reasons is that they are making important decision about career , marriage and life direction.4.solve problems.5.Life experience /Biological conditioning and social conditioning , life stages and attitudes.Exercise 3Sample1.In Chinese culture, fish is a symbol of prosperity. As a dream symbol, fish,particularly salmon, is associated with knowledge and intelligence. If you dream about eating fish, it is believed that you gain knowledge and wisdom.2.In dreams, the snake has many interpretations. It is regarded as a symbol oftemptation or wisdom. It is also interpreted as someone trying to harm you in underhanded or sneaky manner. In Chinese culture, it is believed that snake is a symbol of fortune in a dream.3.The sword in a dream is a symbol of power, authority, protection, or a need tocut away some part or aspect in your life.4.Something that is covered with dust is something that has not been touchedfor a long time. Therefore, dust in a dream may be a symbol of a shut away emotion, fear, or desire within the conscious.5.Houses in dreams are regarded by many psychoanalysts as representing one’spersonality. If you dream about a beautiful house, you could have a positive self-image. If you dream that you keep moving from house to house, you may have been trying different aspects of your personality, or you may be trying to find out what kind of person you are. And the level of the room in the house is believed to indicate the depth of a particular part of personality in you unconscious. But the basement in a dream, for instance, can be as a symbol of the deepest part your personality.6.Death in ad dream can mean the death or change to a part of yourpersonality or the end of a certain phase in your life, For instance, if you dream that a friend dies, it could mean that you have ended up or you have been feeling the need to end up a period of time spent with them.ScriptNew research shows that dreams are often distorted reflections of our daily life. many experts now believe our dreams are so closely related to our waking lives that we canuse them to help us recognize our inner conflicts.According to some experts, men and women dream differently because of biological and social conditioning. In a study of 1000 dreams, half from each sex, experts found that men more often have action dreams .Usually these are set outdoors or in unfamiliar surroundings. Women dream more about emotional struggles with loved ones, usually in indoor settings. As more women have careers, their dreams might become more like man’s. Researchers have found that while housewives dream more about children, women in the workplace dream about bosses and colleagues. Small children who are easily scared dream about frightening animals and monsters that that chase and attack them. Teenagers dream about romance and sex.Some dream researchers found in a study that people between 21and 34 have more anxiety over issues of right and wrong in their dreams, possibly because they are making importance decisions about career, marriage and life direction. People of age 35 to 49 are much less hostile toward others in their dreams, perhaps because they are reaching their greatest achievement and have less need for aggression while awake. After age 65, anxiety about aging appears much more often in people’s dreams.If life stages affect our dreams, so do out attitudes. Studies show that angry people act out their anger in their dreams, and depressed people sometimes dream they are victim of rejection.Creative people often use their dreams to solve problems. According to the author Naomi Epel, when some writers, artists or scientists go to sleep, they ask their subconscious for a dream that will help them solve problems.Listening IIIKeysExercise 1√2, √3, √6Exercise 2CBCACExercise 3SampleAdvantages of daydreaming●It helps kill boring time.●It helps children develop and explore their imagination.●It can reduce a person’s fear or anxiety.●It can keep us awake under dull conditions.Disadvantages of daydreaming●It can be a waste of time when you spend too much time daydreaming.●Children’s problem-solving skills may weaken if they spend too much time daydreaming instead of putting their imagination into work.●When you realize the wide gap between reality and daydreams, daydreaming can lead to greater anxiety and deeper frustration.●It distracts our attention, and may lead to danger in certain situations, like when we are driving a car.ScriptAlmost all people day dreaming during a normal day. We tend to daydreaming the most during those quiet times when we are alone in our cars, sitting in waiting rooms, or preparing for bed. day dreaming or fantasizing is not abnormal; it is a basic human characteristic. Most people have reported that they enjoy their day dreams . Some people have very probable and realistic daydreams while others have unrealistic fantasies such as inheriting a million dollars.Psychologists report that men daydream as much as women , but subject of their daydreams or fantasies is different. Men day dream more about being heroes and good athletes while women tend to daydream about fashions and beauty. As people grow older, they tend to fantasize less, although it is still common in old age. Older people tend to daydream a lot about the past. daydreaming or fantasizing enters into the games of children. Psychologists believe that it is very important for children to participate in fantasy play . It is a normal part of their development. It helps children develop and explore their imagination.Daydreaming has advantages and disadvantages In some situations it can reduce a person's fear or anxiety. can also keep us entertained or awake under dull or boring conditions. Unfortunately, to engage in a daydream or fantasy, we must divert part of our attention from our environment. When it is important for us to remain alert and pay attention to what is going on around us, day dreaming can cause problems. Listening IVKeysExercise 11) parting2)wrong3) dream4)night5) none6)seem7)shore8) sand9)fingers10) grasp11) save12) waveExercise 1Sample1 The fifth line in the first stanza(诗节), “That my days have been a dream”, indicates that the poet regarded his life as a dream.2 That last two lines of both stanzas are quite similar in the wording “ Is all that we see or seem/ But a dream within a dream,” which means that what we see, appear or hope is even more elusive than the life itself that we are living, and is, therefore, a dream within a dream.3 The “grains of the golden sand”may have referred to the start of the “gold rush”in California in 1848, the year before the poem was written, Another interpretation is that it may symbolize the people or things that the poet had valued and treasured, as he was so eager to “grasp them with a tighter clasp”.4) The “pitiless wave”can be interpreted in two ways. It can be viewed as symbolizing “time”, which is compared to “tide” in the saying “ Time and tide wait for no man”. Or it can be interpreted as “death”, which, just as “time”, sweeps away people around us, no matter how eagerly we’d like them to stay.Exercise 3Sample1 This poem may have been addressed to his beloved (could be his wife) in her death bed, who received a farewell kiss from the poet. This can be seen from the first two lines: “ Take this kiss upon the brow! And, in parting from you now,…”2 The poet’s hope is expressed in the second stanza. He wished that he could hold onto people and things that he treasured. But he could not stop the time and death taking away his beloved, however hard he tried. His helplessness led to his confusion, which can be seen from more questions posed by the poet in the second stanza. Physically, the poem is very interestingly laid out in two stanzas, just like two layers of dreams: the first being “life”, a dream, and the second layer “hope”, a dream within a dream, which is more confusing than the first. This idea is very similar to that in the movie Inception (《盗梦空间》) --- the more layers of dreams have, the less stable they become.3 The poet’s depressing tone may have resulted from his troubled and miserable life since his childhood. He felt betrayed by everyone. His mother, who died when he was a small child; his biological father, who abandoned him; his step father, who never legally adopted him and who, ultimately, cast him adrift; and, aboveall, his young dead wife, a beauty symbolizing purity and peace in his eyes. Life itself had seemingly thwarted (挫败) his every hope and effort.ScriptA Dream Within A DreamTake this kiss upon the brow!And, in parting from you now,Thus much let me avow---You are not wrong, who deemThat my days have been a dream;Yes if hope has flown awayIn a night, or in a day,In a vision, or in none,Is it therefore the less gone?All that we see or seemIs but a dream within a dream.I stand amid the roarOf a surf-tormented shore,And I hold within my handGrains of the golden sand---How few! Yet how they creepThrough my fingers to the deep,While I weep---while I weep!O God! Can I not graspThen with a fighter clasp?O God! Can I not saveOne from the pitiless wave?Is all that we see or seemBut a dream within a dream?Part 3 Viewing, Understanding and SpeakingKeysExercise 1BACDExercise 21.too good to be true2.various kinds of3.igonored4.stand5.has something to do with6.gathering fruit7.can’t afford8.something wrong with9.ripe, at hande trueExercise 4SampleI had a dream after I watched the movie of the Harry Porter series. I was walking down a street when my shoes turned into a pair of roller skates. I skated on the pavement, and saw a section of the road suddenly collapsed. I was about to fall when my roller skaters turned into a broomstick! And before I knew it, I found myself flying in the sky, just as Harry Porter did in the movie.ScriptMary: (She awakes from a sweet dream) Ah…Darling, everything is so wonderful! The sun, the air, the water… I feel as if I were in a dream.John: (He still reads the book with not much response.) A dream? Yes, a dream. Mary: Have a look at the beautiful scenery around you, darling. Don’t you think it’s too good to be true?John: Mm, maybe.Mary: Eh, you aren’t listening to me. What are you reading now?John: (He closes the book.) It’s Freud’s Interpretation of Dreams. Honey, have you ever wondered what’s …what’s the meaning of you dreams? You might get some satisfactory explanations for your dreams from this book, because Freud explains various kinds of dreams in it.Mary: It must be a very interesting book! Otherwise, you wouldn’t have ignored me. It seems to me that I’m not as attractive as Freud.John: Yes, it really is.Mary: Yes? ! You mean I’m not charming enough? I can hardly stand your rudeness. John: Of course not. I mean it’s really an interesting book. Freud says that everything in our dreams has something to do with our real life.Mary: Really? I often dream I’m gathering fruit in an orchard. What does fruit represent in our dreams?John: It predicts good fortune. You’ll be rich, honey.Mary: But the fact is we still can’t afford to buy a house.John: I have to admit that’s absolutely true. I spent about all I had on our honeymoon. Mary: Well, there must be something wrong with your interpretations, darling, I doubt whether dreams can predict the future.John: Before I can be more exact, you have to give me more details.Mary: What further information do you need?John: Well, honey, could you tell me what the color of the fruit is in your dreams? Mary: Er…the fruit doesn’t seem to be ripe. In my dreams, I think it’s green. John: I’ve got it. If the color of the fruit is green, you can’t be rich immediately,because only ripe fruit is interpreted as good fortune at hand.Mary: Oh? Are you sure about that?John: Definitely. I’ve just looked it up in Freud’s book.Mary: Then we’ll just have to wait and see?John: That’s right, honey. Do you have any other happy dreams?Mary: Yes. I had another one just now. It was so sweet that I smiled from ear to ear. Would you like to have another try, Mr. Freud?John:It’s my pleasure, madam. What happened in this dream? I guarantee you I can give you another good explanation.Mary: When I was dozing, I dreamed that you gave me a beautiful diamond necklace as memento of our wonderful honeymoon, what do you think that means?John:(He understands his wife’s actual intention and tries to find a way out.) Er…Er… I’m not sure. Er…maybe I’m not knowledgeable enough! But anyway I can turn to the book for help. Wait a minute!Mary: Take it easy, darling! I’m…I’m sure you know how you can make it come true.John: Too bad!Mary:What’s wrong?John: (He smiles cunningly at his wife.) I’m afraid Freud didn’t tell me how to interpret a daydream, only dreams at night.Mary: Daydream?!John: Yes, it must be a daydream since you had it during the day.Part 3 Video Appreciation and Singing for FunVideo AppreciationKeysExercise 1DEFFExercise 21)Mix the sound2)Drag you back3)seagulls4)taking a walk5)police siren6)pulls off the earphones7)alarming dreamsExercise 31)remained alert2)sounds of danger3)the reason4)are reliant on5)aliveExercise 4Sample●I fell asleep after a session of yoga to a light, soft background music once. Idreamed that I was lying on a beach, basking in the sun, with the waves lapping gently against the rocks, and seagulls flying over me. It was so comfortable and relaxing that I felt energetic again after I woke up from the nap.●I once traveled by train and saw a young mother fast asleep, with thepassengers around chattering away. However, she seemed to be very alert to her 3- or 4-year-old’s cry, even if it was in a very low voice. As I saw it, we can sleep through the sounds that we don’t care about, but tend to be dragged back to wakefulness by sounds that worry us.●I dreamed about taking a math test once before my college entranceexamination. I was still struggling with one tough problem when the bell rang sharply, which signaled the end of the test. I felt like being paralyzed in my seat, unable to move a single inch. When I woke up in misery and sweat, I found the bell was nothing but my alarm clock. To a college entrance exam taker, the bell is indeed a very threatening sound signal.ScriptEpisode 1We live in a world of incessant sounds. During our waking hours, our ears are bombarded with noise. But what happens when we’re asleep? Sleep takes up a third of our lives, and that’s when we’re at our most vulnerable. So our sense of hearing never goes off duty. Even as we sleep our ears detect sounds,and our brain analyses them. But why is it that some noises feature in our dreams, while others can wrench us from our sleep? Weird Science goes into the sleeping brain and our evolutionary past to find out. Every night when we go to sleep our senses shut down, except for our sense of hearing, which stays alert to sounds beyond the bedroom. Sounds are just tiny movements of the air molecules around us, funneled down the ear canal to the eardrum. The moving air makes the eardrum vibrate, and these vibrations are amplified by the tiniest bones in the body and passed to the fluid-filled cochlea. Here, the vibrations send ripples through the fluid which move rows of microscopic hair cells. These create electrical signals sent to the brain.Episode 2The brain may mix the sound into the visuals of your dreams, or drag you back to wakefulness. At Swansea University, Dr. Mrak Blaggrove studies the impact of different noises on the brains of sleeping volunteers. These electrodes allow Mark to monitor Sarah’s brainwaves while she sleeps. Once there are signs that she’s dreaming, he can test the effects of different sounds on her dreams. First she gets a blast of seagulls through her headphones. She sleeps through the noise. But has it changed herdream? (Hi Sarah) Mark waits for a couple of minutes, and then wakes her up and asks what she was dreaming about ( I was on a hilltop…Uh huh). Sarah’s dream was of taking a walk on a windy hilltop. An hour later, Sarah is asleep and dreaming again. Now, the test is a threatening sound --- a police siren. It’s no louder than the seagulls, and for a while, she sleeps through the noise. But then she stirs, and, half-conscious, she pulls off the earphones. Can she remember what she was dreaming about before the noise disturbed her? (Yeah, um ambulances…) Amazingly, even while she was asleep, Sarah heard the sirens and they triggered vivid, alarming dreams. The sound eventually convinced her sleeping brain to wake up.Episode 3So why does the brain deal with sounds in such different ways? The answer can be found in our prehistoric past. Our ancestors needed sleep, but it made them more vulnerable to attack by predators. To safeguard them, their sense of hearing remained alert, listening for the sounds of danger. Now the sounds are different, but the reason for hearing in your sleep is jus the same. For a third of your life, you’re reliant on your sense of hearing to keep you alive. Hopefully!Singing for funLyricsI Have a DreamI have a dream, a song to singTo help me cope with anythingIf you see the wonder of a fairy taleYou can take the future, even if you failI believe in angels, something good in everything I seeI believe in angels, when I know the time is right for meI’ll cross the stream, I have a dreamOh yeahI have a dream, a fantasyTo help me through realityAnd my destination makes it worth the whilePushing through the darkness, still another mileI believe in angels, something good in everything I seeI believe in angels, when I know the time is right for meI’ll cross the stream, I have a dreamI have a dream, a song to singTo help me cope with anythingIf you see the wonder of a fairy taleYou can take the future, even if you failI believe in angels, something good in everything I seeI believe in angels, when I know the time is right for meI’ll cross the stream, I have a dreamI’ll cross the stream, I have a dreamPart 4 Further Speaking and ListeningFurther ListeningListening IKeysExercise 15>7>4>1>6>3>8>2Exercise 2CABDBDCScriptIn 1865 ,in a small town in Germany ,a little boy was very sick. His name was Max Hoffman.“Will our son die ?” Max’s parents asked the doctor.“Maybe,” the doctor said quietly .”Stay with Max .Keep him warm .That’s all you can do .”For three days Max lay in his bed . Then he died .He was only five years old .Max’s parents buried their son in the town cemetery .That night Max’s mother had a terrible dream. She dreamed that Max was moving in his coffin . She screamed in her sleep.“Sh ,sh,” her husband said. “It’s all right .You had a bad dream.”The next night Max’s mother screamed in her sleep again . She had the same terrible dream.On the third night Max’s mother had another bad dream. She dreamed that Max was crying . She got out of bed and got dressed. “Quick! Get dressed ,”she told her husband . “We’re going to the cemetery .I want to see Max. I want to dig up his coffin.”At four o’clock in the morning Max’s parent and a neighbor hurried to thecemetery .They dug up Max’s coffin and opened it . There was Max .He looked dead. But he wasn’t lying on his back . He was lying on his side.Max’s father carried Max home . Then he ran to get the doctor .For an hour the doctor rubbed whisky on Max’s lips and warmed his body. Then Max opened his eyes .Max was alive ! A week later he was playing with his friends.Max Hoffman died—really died—in the United State in 1953. He was 93 year old . Listening IIKeysExercise 1TFFTFTExercise 21)pushing2)away3)friend’s house4)burned to death5)the dead6)in front of7)kid s’ minds8)making moneyScript(A couple is talking about their 8-year-old daughter ,Debbie .They also have a son ,Barry ,who is 16.)Mother : I had to go in to Debbie twice last night .She was having these terrible nightmares! She was screaming and shouting and she kept trying to push me away .She was yelling , “Don’t hurt me ! Don’t hurt me !”Father : What was wrong with her then ?Mother : I don’t know. I couldn’t get a word out of her when she woke up this morningFather: Does Barry know anything about it ? Didn’t she go with him to his friend’s yesterday afternoon ? Wait a minute , I’ll give him a shout . Barry ! Come here , Will you ?Barry: What’s up?Father: Didn’t you say you were going to watch a video at your friend’s yesterday?Mother: Well, what exactly did you watch ? Debbie’s been having the most terrible nightmares.Barry: Oh, I don’t know ! Some film his dad had left lying around . About a man who had been burned to death in a car crash, who came back from the dead to take revenge on young girls . He tears them to bits and eats them. It was a young girl , see , who ran in front of his car and made him crash . Don’t know why it’s giving her nightmares. It was really stupid , if you ask me ! Anyway, she didn’t have to watch it . did she ?Mother:You should have more sense at your age . You should have stopped her watching it.Father: I blame the people who made films like that. They shouldn’t be allowed to make them . They must be really sick! All they care about is making money –they don’t care they are doing to kid s’ minds.Listening IIIKeysExercise 1ACDBCExercise 2TTTT FFTTScriptDear Editor,Your paper is great . I read with great interest your interpretation of dreams of teeth falling out .It is the same interpretation that many others use as well : needing to be heard etc. I myself had this dream repeatedly and was dying to know what it meant , as is was always confusing and disturbing . However , I was always unsatisfied with the “ needing to be heard ” thing.Your might note that many people who have this dream are feeling worried , depressed or frightened as their teeth are falling out painlessly .Sometime they even try to keep the teeth from falling out . Finally I came up with a different interpretation , which fitted me much better . In fact , I’ve had fewer dreams of this so rt now .So I thought you might be interested .For me , the dream means I am talking TOO MUCH . It means thoughtlessness ,telling secrets , gossiping unwisely . And it’s my subconscious warning me .Now ,if I have this dream ,I know I have been unwise with my big mouth ! Trying to cram the teeth back in , or stop them falling out ,or trying to find a dentist , actually means trying to stop the words or gossip from coming out , and the feelings of depression are reflecting the regret of being too revealing –usuallyto an enemy . I am much more aware of this now and not such a big mouth ! Maybe you could add to your interpretation,Best,KatieListening IVKeysExercise 1DCBDExercise 2TFTFFTScriptSleep is something we generally associate with living creatures. Of course, it is true that a lot of animals sleep, but zoologists are not certain that primitive forms of animals life, like worms and snails, even really sleep. On the other hang, animals such as bears sleep for 4 or 5 months every year.The amount of sleep a human being needs depends on age, the individual and possibly race. .For example, doctors think that pre-school children need between 10 and12 hours a night; school children between 9 and 11 hours, and adults between 7and9 hours. There are exceptional cases of old people who sleep only between 2 and 3 hours a day and continue to be active and healthy. The sleep requirements of different races also appear to be different. Japanese people, for example, sleep, sleep fewer hours than Europeans.It is not known for certain if certain if mental activity (apart from dreaming) occurs when a person is asleep. However, it is certainly true that some people can wake up at a specific, pre-determined time. There are also stories about mathematicians who solve difficult problems during sleep, because their subconscious minds continue working on the problem.Some types of unpleasant dreams (or ‘‘nightmares’’)are quite common, the dreams is taking a test, but is not properly prepared. he is falling from a tree ,or an animal or thing is chasing him. Some people say these last two occur because man’s ancestors lived in trees and were in constant danger from wild animals.。
全新版大学英语综合教程3(第二版)课后答案解析全集
全新版大学英语综合教程3(第二版)课后答案解析全集简介《全新版大学英语综合教程3(第二版)》是一本适用于大学生的英语综合教材，旨在帮助学生提高英语听说读写能力。
本文档提供了此教材中课后习题的答案解析，为学生提供了方便和参考。
目录1.第一单元：单词与短语学习2.第二单元：听力训练3.第三单元：阅读理解4.第四单元：语法与词汇5.第五单元：写作训练6.第六单元：听力训练7.第七单元：阅读理解8.第八单元：语法与词汇9.第九单元：写作训练10.第十单元：听力训练…（省略部分单元）第一单元：单词与短语学习1.1 词汇选择1.A2.B3.A4.C5.B解析： - 1. A选项符合句意，表示某物“连在一起”。
- 2. B 选项符合句意，表示“建立/创立”。
- 3. A选项符合句意，表示“表达”。
- 4. C选项符合句意，表示“有目的的”。
- 5. B选项符合句意，表示“应急”。
1.2 短语选择1.C2.A3.B4.B5.A解析： - 1. C选项符合句意，表示“追赶”。
- 2. A选项符合句意，表示“从……出来”。
- 3. B选项符合句意，表示“辨认出”。
- 4. B选项符合句意，表示“犯错误”。
- 5. A选项符合句意，表示“不久”。
第二单元：听力训练2.1 听对话，选择正确答案1.B2.A3.C4.B5.B解析： - 1. B选项符合对话内容，表示原来他们“想要去参观”。
- 2. A选项符合对话内容，表示她们“去看医生”。
- 3. C选项符合对话内容，表示他们“在机场见面”。
- 4. B选项符合对话内容，表示他会“坚持下去”。
- 5. B选项符合对话内容，表示他喜欢“阅读”。
2.2 听长对话，回答问题1.Yes, the woman does like coffee.2.The woman prefers tea to coffee.3.The woman will have a cup of tea.4.The woman has a cup of coffee every morning.5.Yes, the woman has had coffee before.解析：- 1. 对话中女士提到她喜欢咖啡，所以答案为“Yes”。
新标准大学英语综合教程4(unit1-6)课后答案及课文翻译
Key to book4 unit1-6Unit 1Active reading (2)8 Look at the sentences from the passage and identify the style features.1 Twelve years at school and three years at university, teachers banging on about opportunities in the big wide world beyond our sheltered life as students, and what do I find?This shows the informality of an incomplete sentence in the first part, the use of an informal expression (banging on) and a rhetorical question to the reader (What do I find?)2 Try as I might to stay cheerful, all I ever get is hassle, sometimes with people (especially boys, god, when will they grow up?) …This has the use of an informal word (hassle), an informal exclamation (god) and a question to the reader (When will they grow up?)3 Actually, I had my eye on the course at the London School of Economics (LSE).Here there is a discourse marker typical of speech (Actually) and an informal phrase (had my eye on).4 I kind of understand it, and not just because my degree is in economics.Here “kind of” is a sort of discourse marker of informal speech (showing something is general, vague or not definite).5 I wanted something in finance and investments, because you know, maybe with a job like that, I could use my degree.This has a discourse marker of informal speech (you know).6 ... it’s true, he really did seem to have three hands.Again here is a discourse marker of informal speech (it’s true).7 I talked to him about ... well, about pretty well everything …This has another discourse marker of informal speech (well) and an informal phrase (pretty well).Language in usetry as … might3 Rewrite the sentences using try as … might .1 I’m trying to fill this last page, but I just can’t think of anything.Try as I might to fill this last page, I just can’t think of anything.2 I try to be friendly with Marta, but she doesn’t seem to respond.Try as I might to be friendly with Marta, she doesn’t seem to respond.3 I try hard to get to sleep, but I can’t help thinking about my family.Try as I might to get to sleep, I can’t help thinking about my family.4 He just doesn’t seem to get the promotion he deserves, even though he keeps trying.Try as he might, he just doesn’t seem to get the promotion he deserves. / Try as he might to get the promotion he deserves, he just d oesn’t seem to get it.5 I keep trying to remember her name, but my mind is a blank.Try as I might to remember her name, my mind is a blank.given that …4 Rewrite the sentences using given that …1 Since I know several languages, I thought I would look for work abroad.Given that I know several languages, I thought I would look for work abroad.2 Xiao Li has the best qualifications, so she should get the job.Given that Xiao Li has the best qualifications, she should get the job.3 Since we’re all here, I think it would be a good idea to get down to some work.Given that we’re all here, I think it would be a good idea to get down to some work.4 Since it’s rather late, I think we should leave this last task until tomorrow.Given that it’s rather late, I t hink we should leave this last task until tomorrow.clauses introduced by than5 Rewrite the sentences using clauses introduced by than .1 She’s experienced at giving advice. I’m more experienced.She’s less experienced at giving advice than I am. / I’m more experienced at giving advice than she is.2 You eat too much chocolate. It isn’t good for you.You eat too much chocolate than is good for you.3 She worked very hard. Most part-timers don’t work so hard.She worked harder than most part-timers do.4 You have arrived late too many times. That isn’t acceptable.You have arrived late more times than is acceptable.5 I don’t think you should have given so much personal information. It isn’t wise.I think you have given more personal information than is wise.collocations6 Read the explanations of the words. Answer the questions.1 highlight A highlight is the most exciting, impressive, or interesting part of an event.(a) What would you like to be the highlight of your career?I would like the highlight of my student career to be to receive a national award for the best student research project.(b) How can you highlight an important sentence in a text?You can underline it in pencil or pen or you can use coloured pens or highlighters.(c) What are the edited highlights of a football match?The highlights are when someone scores a goal or prevents one from being scored.2 loan A loan is an amount of money someone borrows from someone else.(a) Have you ever taken out a loan?No, I haven’t. But my parents have taken out several loans to buy kitchen equipment.(b) What is the best way to pay off a loan?It is best to pay a loan off quickly, although you will still have to pay some interest.(c) If you have a library book on loan, what do you have to do with it?You have to return it before the date it is due, otherwise you may have to pay a fine.3 thrive To thrive means to be very successful, happy or healthy.(a) What sort of business thrives best in your part of the country?In my part of the country, light industries and electronics companies thrive.(b) Which sort of plants thrive in a hot climate?In a hot climate you can see tropical fruit and vegetables thrive and also tropical plants and trees.(c) Why do you think some couples thrive on conflict?It is difficult to understand why some couples thrive on conflict. Maybe each one wants to compete with the other or maybe they enjoy “kissing and making up” after the conflict.7 Translate the paragraphs into Chinese.If you ask me, real life is not all it’s cracked up to be. Twelve years at school and three years at university, teachers banging on about opportunities in the big wide world beyond our sheltered life as students, and what do I find?Try as I might to stay cheerful, all I ever get is hassle, sometimes with people (especially boys, god, when will they grow up?), but mostly with money. It’s just so expensive out here! Everyone wants a slice off you. The Inland Revenue wants to deduct income tax, the bank manager wants repayments on my student loan, the landlord wants the rent, gas, water, electricity and my mobile bills keep coming in, and all that’s before I’ve had anything to eat. And then some bright spark calls me out of the blue, asking if I’m interested in buying a pension. At this rate, I won’t even last till the end of the year, let alone till I’m 60.（☞翻译时可以根据上下文增译，即增加原文暗含了但没有直接表达出来的意思。
大学课本习题答案---应该说如果下面还找不到的那么肯定答案还没出了
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新标准大学英语综合教程3、4课后翻译答案
新标准大学英语综合教程3课后翻译答案Unit11对于是否应该在大学期间详细规划自己的未来，学生们意见不一。
有的人认为对未来应该有一个明确的目标和详细的计划，为日后可能遇到的挑战做好充分的准备；有的人则认为不用过多考虑未来，因为未来难以预料。
(map out; brace oneself for; uncertainty)Students differ about whether they should have their future mapped out when they are still at university. Some think they should have a definite goal and detailed plan, so as to brace themselves for any challenges, whereas some others think they don’t have to think much about the future, because future is full of uncertainties.2 经过仔细检查，这位科学家得知自己患了绝症。
虽然知道自己将不久于人世，他并没有抱怨命运的不公，而是准备好好利用剩下的日子，争取加速推进由他和同事们共同发起的那个研究项目，以提前结项。
( tick away; make the best of; have a shot at)After a very careful check-up, the scientist was told he had got a fatal disease. Although he knew that his life was ticking away, instead of complaining about the fate, the scientist decided to make the best of the remaining days, and speed up the research project he and his colleagues initiated, and have a shot at completing it ahead of schedule.Unit21在火车站上，有一位老人给我讲述了他参加解放战争的经历，那些战斗故事对我有着极大的吸引力。
新标准大学英语综合教程4课后习题翻译答案
新标准大学英语综合教程4课后习题翻译答案UNIT11.我认为，选修第二专业并不适合每一位本科生。
If you ask me, takinga second major isn’t good for every undergraduate.2.我大学本科主修英语专业，大一时就开始辅修经济学了。
In myfreshman year as an English major, I took economics as my minor.3.无疑，我是班里最用功的学生。
By all odds, I was the mosthardworking student in my class.4.我竭尽全力想同时达到两个不同专业的要求，但还是有不及格的时候。
But try as I might to meet the requirements of the two different subjects, I still couldn’t do well enough to pass all the exams.5.因为经济学需要良好的数学基础，我不得不花大量时间钻研数学，因而忽略了英语学习。
Given that the study of economics required a good command of mathematics, I had to spend so much time on math that I neglected my English major.6.第二学期,《英国文学》及《宏观经济学》两门课不及格给我敲响了警钟，Failing English Literature and Macroeconomics in the second semester sounded the alarm for me.7.这可是我一生中第一次考试不及格，这大大打击了我的自信心。
Thiswas the first time I did not pass a course in my life, which had greatly sapped my confidence.8.虽然我不是一个容易向命运低头的人，在暑假结束的时候，我还是决定放弃经济学，以免两个专业都难以完成。
2023大学_数学专业英语试题及参考答案
2023数学专业英语试题及参考答案数学专业英语试题一、词汇及短语1. For a long period of the history of mathematics, the centric place of mathematical methods was occupied by the logical deductions “在数学史的很长的时期内，是逻辑推理一直占据数学方法的中心地位”2. An equation is a statement of the equality between two equal numbers or number symbols.equation ：“方程”“等式”等式是关于两个数或数的符号相等的'一种陈述3. In such an equation either the two members are alike, or become alike on performance of the indicated operation. 这种等式的两端要么一样，要么经过执行指定的运算后变成一样。
注“two members”表等号的两端alike 相同的一样的On the performance of …中的“on”引导一个介词短语做状语Either…or…4. is true “成立”5. to more and change the terms移次和变形without making the equation untrue 保持方程同解数学专业英语试题二、句型及典型翻译1. change the terms about 变形2. full of ：有许多的充满的例 The streets are full of people as on a holiday(像假日一样，街上行人川流不息)3. in groups of ten…4. match something against sb. “匹配”例 Long ago ,when people had to count many things ,they matched them against their fingers. 古时候，当人们必须数东西时，在那些东西和自己的手指之间配对。
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西南财经大学研究生入学考试历年真题及答案
西南财经大学研究生入学考试历年真题及答案在西南财经大学研究生入学考试中，历年的真题对于考生来说是非常宝贵的资源。
通过研究真题，考生可以了解考试形式、考察内容和答题技巧，从而更好地备考和提高自己的分数。
本文将为大家整理并介绍西南财经大学研究生入学考试的历年真题及答案。
第一部分：数学在西南财经大学研究生入学考试中，数学是必考科目之一。
历年的数学真题涵盖了多个知识点，包括微积分、线性代数、概率统计等。
考生可以通过研究真题，了解考试的重点和难点，并针对性地进行复习。
以下是2016年数学真题的一道选择题：1. 设函数 $y = ax^2 + bx + c$，其中 $a > 0$，当 $x \in [-1, 1]$ 时，函数 $y$ 的值单调递减，则下列结论正确的有（）A. $b > 0$B. $b < 0$C. $b = -2a$D. $c > 0$答案：B解析：根据函数 $y = ax^2 + bx + c$ 单调递减的特点，可知二次项的系数 $a > 0$，且一次项的系数 $b < 0$，故答案为 B。
通过研究上述题目及其答案，考生可以了解到在判断函数单调性时，需要对函数的二次项系数和一次项系数进行分析。
第二部分：英语英语是西南财经大学研究生入学考试的另一门必考科目。
历年的英语真题主要考察考生的阅读理解、词汇运用和语法等方面的能力。
阅读真题能够帮助考生提高阅读速度和理解能力，积累词汇，并熟悉英语语法。
以下是2018年英语真题的一道阅读理解题：2. According to the passage, the foundation of Chinese age is based on （）A. mythology and legendsB. astronomical phenomenaC. historical eventsD. documentation答案：B解析：根据文章内容可知，中国的年龄计算是基于天文现象的，故答案为 B。
高三英语爱好与大学专业选择关系分析练习题30题带答案解析
高三英语爱好与大学专业选择关系分析练习题30题带答案解析1. Tom is interested in music. He might choose a major related to _____.A. literatureB. mathematicsC. musicologyD. physics答案解析：C。
“musicology”是音乐学的意思，与对音乐感兴趣相对应。
“literature”是文学；“mathematics”是数学；“physics”是物理，都与音乐爱好不相关。
2. Lily loves painting. Which major could be a good choice for her?A. engineeringB. chemistryC. fine artsD. computer science答案解析：C。
“fine arts”是美术的意思，与喜欢绘画的爱好相匹配。
“engineering”是工程学；“chemistry”是化学；“computer science”是计算机科学，都与绘画爱好无关。
3. Mark is crazy about sports. He may consider a major in _____.A. historyB. geographyC. physical educationD. biology答案解析：C。
“physical education”是体育教育，与热爱体育的爱好相符。
“history”是历史；“geography”是地理；“biology”是生物学，都与体育爱好不相关。
4. Amy enjoys reading books. She could choose a major like _____.A. business administrationB. sociologyC. English literatureD. architecture答案解析：C。
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大学数学，专业英语课后答案2.1 数学、方程与比例（1）数学来源于人类的社会实践，包括工农业的劳动，商业、军事和科学技术研究等活动。
Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches.（2）如果没有运用数学，任何一个科学技术分支都不可能正常地发展。
No modern scientific and technological branches could be regularly developed without the application of mathematics.（3）符号在数学中起着非常重要的作用，它常用于表示概念和命题。
Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often.（4）17 世纪之前，人们局限于初等数学，即几何、三角和代数，那时只考虑常数。
Before 17th century, man confined himself to the elementary mathematics, i. e. , geometry, trigonometry and algebra, in which only the constants were considered.（5）方程与算数的等式不同在于它含有可以参加运算的未知量。
Equation is different from arithmetic identity in that it contains unknown quantity which can join operations. （6）方程又称为条件等式，因为其中的未知量通常只允许取某些特定的值。
Equipment is called an equation of condition in that it is true only for certain values of unknown quantities in it. （7）方程很有用，可以用它来解决许多实际应用问题。
Equations are of very great use. We can use equations in many mathematical problems.（8）解方程时要进行一系列移项和同解变形，最后求出它的根，即未知量的值。
To solve the equation means to move and change the terms about without making the equation untrue, until the root of the equation is obtained, which is the value of unknown term.2.2 几何与三角（1）许多专家都认为数学是学习其他科学技术的必备基础和先决条件。
Many experts recognize that mathematics is the necessary foundation and prerequisite of studying other science technology.（2）西方国家的专家认为几何起源于巴比伦和埃及人的土地测量技术，其实中国古代的数学家对几何做了许多出色的研究。
The western experts think that geometry had its origin in the measurements by the Babylonians and Egyptians of their lands. Infect, the ancient Chinese mathematicians made much remarkable study for geometry.（3）几何的学习使学生在思考问题时更周密和审慎，他们将不会盲目接受任何结论。
In studying geometry, the student is taught to think clearly and critically and he is led away from the practice of blind acceptance of any conclusions.（4）数学培养学生的分析问题的能力，使他们能应用毅力、创造性和逻辑推理来解决问题。
Studying mathematics can develop the students’ ability to analyze problems and utilizing perseverance, originality, and logical reasoning in solving the problem.（5）几何主要不是研究数，而是形，例如三角形，平行四边形和圆，虽然它也与数有关。
Geometry mainly studies hot numbers but figures such as triangles, parallelograms and circles, though it is related with numbers.（6）一个立体（图形）有长、宽和高；面（曲面或平面）有长和宽，但没有厚度；线（直线或曲线）有长度，但既没有宽度，也没有厚度；点只有位置，却没有大小。
A solid (figure) has length, width and height. A surface (curved surface or plane surface) has length and width, but no thickness. A line (straight line or curved line) has length, but no width and thickness. A point has position, but no dimension.（7）射线从某个点出发无限延伸；两条从同一点出发的射线构成了角。
这两条射线称为这个角的两边，当这两边位于同一直线上且方向相反时，所得的角是平角。
A ray starts from a point and extends infinitely far. Two rays starting from one point form an angle, which are called two edges of the angle. When two edges lie in the same line and have opposite direction named plane angle. （8）平面上的闭曲线当其中每一点到一个固定点的距离均相等时叫做圆。
这个固定点称为圆心，经过圆心且其两个端点在圆周上的线段称为这个圆的直径，直径的一半叫做半径，这条曲线的长度叫做周长。
A circle is a closed curve lying in one plane, all points of which are equidistant from a fixed point. The fixed point called the center. A diameter of a circle is a line segment through the center of the circle with endpoints on the circle. Half of the diameter is called radius. The length of the circle is called circumference.2.3 集合论的基本概念（1）由小于10 且能被3 整除的正整数组成的集是整数集的子集。
The set consisting of those positive integers less than 10 which are divisible by 3 is a subset of the set of all integers.（2）如果方便，我们通过在括号中列举元素的办法来表示集。
When convenient, we shall designate sets by displaying the elements in braces.⊆表示集的包含关系，也就是说，式子A ⊆ B 表示A 包含于B。
（3）用符号The relation ⊆is referred to as set inclusion; A⊆B means that A is contained in B.⊆ B 并不排除B ⊆ A 的可能性。
（4）命题AThe statement A⊆B does not rule out the possibility that B⊆A.（5）基础集可根据使用场合不同而改变。
The underlying set may vary from one application to another according to using occasions.（6）为了避免逻辑上的困难，我们必须把元素x 与仅含有元素x 的集{x}区别开来。
To avoid logical difficulties, we must distinguish between the element x and the set {x} whose only element is x. （7）图解法有助于将集合之间的关系形象化。
Diagrams often help using visualize relationship between sets.（8）定理的证明仅仅依赖于概念和已知的结论，而不依赖于图形。
The proofs of theorems rely only on the definitions of the concepts and known result, not on the diagrams.2.4 整数、有理数与实数整数（1）严格说，这样描述整数是不完整的，因为我们并没有说明“依此类推”或“反复加1” 的含义是什么。