lab21麻省理工研究生试卷

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2021MBA英语真题英语

2021年研究生入学统一考试试题（英语二）Section I Use of EnglishDirections：Read the following text. Choose the best word (s) for each numbered blank and mark A, B, C or D on the ANSWER SHEET. (10 points)Why do people read negative Internet comments and do other things that will obviously be painful? Because humans have an inherent need to 1 uncertainty, according to a recent study in Psychological Science. The new research reveals that the need to know is so strong that people will 2 to satisfy their curiosity even when it is clear the answer will 3.In a series of four experiments, behavioral scientists at the University of Chicago and the Wisconsin School of Business tested students' willingness to 4 themselves to unpleasant stimuli in an effort to satisfy curiosity. For one 5 each participant was shown a pile of pens that the researcher claimed were from a previous experiment. The twist?Half of the pens would 6 an electric shock when clicked.Twenty-seven students were told which pens were electrified;another twenty-seven were told only that some were electrified 7 left alone in the room, the students who did not kn ow which ones would shock them clicked more pens and incurred more shocks than the students wh o knew what would 8 .Subsequent experiments reproduced this effect with other stimuli, 9 the sound of fingernails on a chalkboard and photographs of disgusting insects.The drive to 10 is deeply rooted in humans,much the same as the basic drives for 11 or shelter,sa ys Christopher Hsee of the University of Chicago. Curiosity is often considered a good instinct-it can 12new scientific advances, for instance-but sometimes such 13 can insight that curiosity can drive you to do 14 things is a profound curiosit y is possible to 15 ,however. In a final experiment,participants who were encouraged to 16 how they would feel after viewing an unpleasant picture were less likely to 17 to see such an results suggest th at imagining the 18 of following through on one's curiosity ahead of time can help determine 19 it is worth the endeavor. Thinking about long-term 20 is key to reducing the possible negative effects of curiosity."Hsee other words,don't read onli ne comments.1. A. resolve B. protect C. discuss D. ignore. refuse B. wait C. seek D. regret. rise B. last C. mislead D. hurt. alert B. tie C. expose D .treat. message B. trial C. review D. concept. remove B. weaken C. deliver D. interrupt7. A. Unless B. If C. Though D. When8. A. happen B. continue C. disappear D. change9. A. rather than B. such as C. regardless of D. owing to10. A. disagree B. forgive C. forget D. discover11. A. pay B. marriage C. food D. schooling. begin with B. rest on C. learn from D. lead to. withdrawal B. inquiry C. persistence D. diligence. self-destructive B. self-reliant C. self-evident D. self-deceptive. resist B. define C. replace D. trace. predict B. overlook C. design D. conceal17. A. remember B. choose C. promise D. pretend18. A. relief B. plan C. outcome D. duty. whether B. why C. where D. how20. A .limitations B. investments C. strategies D. consequencesSection Ⅱ Reading ComprehensionPart ADirections:Read the following four texts. Answer the questions below each text by choosing A, B, C or D. Mark your answers on the ANSWER SHEET. （40 points）Text 1It is curious that Stephen Koziatek feels almost as though he has to justify his efforts to give his students a better future.is part of something pioneering. He is a teacher at a New Hampshire high school where learning is not something of books and tests and mechanical memorization, but practical. When did it become accepted wisdom that students should be able to name the 13th president of the United States but be utterly overwhelmed by a broken bike chain?As Koziatek knows, there is learning in just about everything. Nothing is necessarily gained by forcing students to learn geometry at a graffitied desk stuck with generations of discarded chewing gum. They can also learn geometry by assembling a bicycle.But he’s also found a kind of insidious prejudice. Working with your hands is seen as almost a mark of inferiority. Schools in the family of vocational education “have that s tereotype, that it’s for kids who can’t make it academically,” he says.On one hand, that viewpoint is a logical product of America’s evolution. Manufacturing is not the economic engine that it once was. The job security that the US economy once offered to high school graduates has largely evaporated. More educationis the new principle. We want more for our kids, and rigitfully so.But the headlong push into bachelor’s degrees for all -and the subtle devaluing of anything less-misses an important point: That’s not the only thing the American economy needs. Yes, a bachelor’s degree opens more doors. But even now, 54 percent of the jobs in the country are middle-skill jobs, such as construction and high-skill manufacturing. But only 44 percent of workers are adequately trained.In other words, at a time when the working class has turned the country on its political head, frustrated that the opportunity that once defined America is vanishing, one obvious solution is staring us in the face. There is a gap in working-class jobs, but the workers who need those jobs most aren’t equipped to do them. Koziatek’s Manchester School of Technology High School is trying to fill that gap.Koziatek’s school is a wake-up call. When education becomes one-size-fits-all, it risks overlooking a nation’s diversity of gifts.21. A broken bike chain is mentioned to show students’ lack of______.A. mechanical memorizationB. academic trainingC. practical abilityD. pioneering spirit22. There exists the prejudice that vocational education is for kids who______.A. are financially disadvantagedB. are not academically successfulC. have a stereotyped mindD. have no career motivation23. We can infer from Paragraph 5 that high school graduates______.A. are entitled to more “educational privilegesB. are reluctant to work in manufacturingC .used to have more job opportunitiesD. used to have big financial concerns24. The headlong push into bachelor’s degrees for all_____.A. helps create a lot of middle-skill jobsB. may narrow the gap in working-class jobsC. is expected to yield a better-trained workforceD. indicates the overvaluing of higher education25. The author’s attitude toward Koziatek’s school can be described as_____.A. supportiveB. disappointedC. tolerantD. cautiousText2While fossil fuels- coal, oil, gas- still generate roughly 85 percent of the world's energy supply, it's clearer than ever that the future belongs to renewable sources such as wind and solar. The move to renewables is picking up momentum around the world: They now account for more than half of new power sources going on line.Some growth stems from a commitment by governments and farsighted Business to fund cleaner energy sources. But increasingly the stories about the plummeting prices of renewables, especially wind and solar. The cost of solar panels has dropped by 80 percent and the cost of wind turbines by close to one-third in the past eight years.In many parts of the world renewable energy is already a principal energy source. In Scotland, forexample, wind turbines provide enough electricity to power 95 percent of homes. While the rest of the world takes the lead, notably China and Europe, the United States is also seeing a remarkable shift. In March, for the first time, wind and solar power accounted for more than 10 percent of the power generated in the US ,reported the US Energy Information Administration.President Trump has underlined fossil fuels - especially coal - as the path to economic growth. In a recent speech in Iowa, he dismissed wind power as an unreliable energy source, But that message did not play well with many in Iowa, where wind turbines dot the fields and provide 36 percent of the state's electricity generation - and where tech giants like Microsoft are being attracted by the availability of clean energy to power their data centers.The question “what happens when the wind doesn't blow or the sun doesn'tshine?" has provide d a quick put-down for skeptics. But a boost in the storage-capacity of batteries is making their ability to keep power flowing around the clock more likely.The advance is driven in part by vehicle manufacturers, who are placing big bets on battery-powered electric vehicles. Although electric cars are still a rarity on roads now, this massive investment could change the picture rapidly in coming years.While there's a long way to go, the trend lines for renewables are spiking. The pace of change in energy sources appears to be speeding up perhaps: just in time to have a meaningful effect in slowing climate change. What Washington does-or doesn't do- to promote alternative energy may mean less and less a time of a global shift in thought.26. The word "plummeting"(Line 3, is closest in meaning to ______A. stabilizingB. changingC. fallingD. rising27. According to Paragraph 3, the use of renewable energy in America ______A. is progressing notablyB. is as extensive as in EuropeC. faces many challengesD. has proved to be impractical28. It can be learned that in Iowa,______.A. wind is a widely used energy sourceB. wind energy has replaced fossil fuelsC. tech giants are investing in clean energyD. there is a shortage of clean energy supply29. Which of the following is true about clean energy according to Paragraphs 5&6?A. Its application has boosted battery storage.B. It is commonly used in car manufacturing.C. Its continuous supply is becoming a reality.D. Its sustainable exploitation will remain difficult.30. It can be inferred from the last paragraph that renewable energy _____.A. will bring the US closer to other countriesB. will accelerate global environmental changeC. is not really encouraged by the US governmentD. is not competitive enough with regard to its costText 3The power and ambition of the giants of the digital economy is astonishing —Amazon has just announced the purchase of the upmarket grocery chain Whole Foods for $, but two years agoFacebook paid even more than that to acquire the WhatsApp messaging service, which doesn’t have any physical product at all. What WhatsApp offered Facebook was an intricate and finely detailed web of its user s’ friendships and social lives.Facebook promised the European commission then that it would not link phone numbers to Facebook identities, but it broke the promise almost as soon as the deal went through. Even without knowing what was in the messages, the knowledge of who sent them and to whom was enormously revealing and still could be. What political journalist, what party whip, would not want to know the makeup of the WhatsApp groups in which Theresa May’s enemies are currently plotting? It may be that the value of Whole Foods to Amazon is not so much the 460 shops of owns, but the records of which customers have purchased what.Competition law appears to be the only way to address these imbalances of power. But it is clumsy. For one thing, it is very slow compared to the pace of change within the digital economy. By the time a problem has been addressed and remedied it may have vanished in the marketplace, to be replaced by new abuses of power. But there is a deeper conceptual problem, too. Competition law as presently interpreted deals with financial disadvantage to consumers and this is not obvious when the users of these services don’t pay for them. The users of their services are not their customers. That would be the people who buy advertising from them —and Facebook and Google, the two virtual giants, dominate digital advertising to the disadvantage of all other media and entertainment companies.The product they’re selling is data, and we, the users, convert our lives to data for the benefit of the digital giants. Just as some ants farm the bugs called aphids for the honeydew they produce wheto Paragraph1，Facebook acquired WhatsApp for its 。

麻省理工数学真题答案解析

麻省理工数学真题答案解析作为世界顶尖的科学技术机构之一，麻省理工学院的数学课程一直备受瞩目。

其数学考试着重培养学生的综合分析能力和解决问题的能力，因此，麻省理工数学真题对于广大数学爱好者来说具有参考价值。

在本文中，我们将通过解析一道麻省理工数学真题，探讨该题的解法和答案，帮助读者更好地理解数学思维和应用。

让我们先来看一道典型的麻省理工数学真题：题目：某城市一年365天，每一天的天气要么是晴天要么是雨天。

如果没有任何规律可循，每一天的天气状况是独立且随机的。

已知该城市每年的晴天和雨天的比例为3:2，假设每个月有30天，请问该城市在某一月份中连续五天的天气都是晴天的概率是多少？解析：首先，我们需要了解一些基本概念。

题目中给出了该城市每年的晴天和雨天的比例为3:2，也就是说每年有5n天是晴天，3n天是雨天，其中n是任意正整数。

又已知每个月有30天，所以我们可以确定每个月的晴天和雨天的天数分别为18n和12n。

现在，我们的目标是求解该城市某一月份中连续五天都是晴天的概率。

为了做到这一点，我们需要找到这种情况可能出现的具体组合。

假设某个月的晴天和雨天分别用字母"S"和"R"表示，例如，连续五天都是晴天可以表示为"SSSSS"。

为了找出可能的组合，我们可以将连续五天的天气情况分为两类，一类是当第一个和最后一个都是晴天时，另一类是当第一个和最后一个都是雨天时。

对于第一类情况，我们可以从该月的第一天开始，连续五天都是晴天的概率为(18n/30) * (18n/30) * (18n/30) * (18n/30) *(18n/30)。

这里的18n/30表示某一天是晴天的概率。

因为每一天的天气状况是独立且随机的，所以连续五天都是晴天的概率可以通过连续五个晴天的概率相乘得到。

对于第二类情况，与第一类情况类似，我们可以从该月的第一天开始，连续五天都是雨天的概率为(12n/30) * (12n/30) * (12n/30) * (12n/30) * (12n/30)。

2021年研究生英语模拟试卷与答案解析(15)

2021年研究生英语模拟试卷与答案解析15一、单选题(共40题)1.Recognizing when a friend or colleague feels sad,angry or surprised is key to getting along with orhers.1 a new study suggests that a skill for listening in on feelings may sometimes come with an extra dose of stress.This and other research 2 the prevailing view that emotional intelligence is uniformly 3 to its bearer.In a study published in the September 2021 issue of E7notion,psychologists Myriam Bechtoldt and Vanessa Schneider asked 166 male university students a series of questions to 4 their emotional smarts.5,they showed the students photographs of people's faces ancl askecl them 6 what extent feelings such as happiness or disgust were being expressed.The students 7 had to give job talks in front of judges displaying stern facial expressions.The scientists measured concentrations of the stress hormone cortisol in the students'saliva before and after the talk.In students who were 8 more emotionally intelligent,the stress measures increased more during the experiment and took 9 to go back to baseline.The 10 suggest that some people may be too emotionally clever for their own good,says Hillary Anger Elfenbein,a professor of organizational behavior at Washington University inSt.Louis."Sometimes you can be so good at something 11 it causes trouble,"she notes.Indeed,the study adds to previous research hinting at a（n）12 side of emotional intelligence.A study published in 2002 in Pers'onalr.t,y and Individual Di f ferences suggested that emotionally 13 people might be particularly 14 to feelings of depression and hopelessness.15,several studies,including one published in 2013 in PLOS ONE,have implied that emotional intelligence can be used to manipulate others for personal 16.More research is needed to see how exactly the relation between emotional intelligence and stress woulcl 17 0ut in women anclin people 18 different ages and education levels.19,emotional intelligence is a useful skill to have,as long as you learn to also properly 20 emotions-both others'and your own.8选？A：labeledB：perceivedC：ratedD：acknowledged【答案】：C【解析】：本题考查上下文语义一动词词义辨析。

MIT微观试卷exam1_topics

Topic Review: 14.04 MidtermI. Consumer Thoery: 75-85% of TestA. Construction of Utility Functions1.Requirements for the construction of a utility function2.Requirements for budget exhaustion3.Proving Convexity and Monotinicity of indifference curves (Two Good Case)4.Ordinal vs Cardinal Preferences5.Requirements for vNM utility functions (Expected Utility)B. Utility Maximization1.Utility Maximization/Indirect Utility Functions2.Expenditure Minimization3.Marshallian/Hicksian Demand Functions4.Envelope Theorem (Shephard’s Lemma)5.Kuhn-Tucker Optimization (At least know how to formally solve quasi-linear,leontieff, linear, Cobb Douglas. Problems will be similar, but not exactly thesame as these)6.Marginal Rate of Substitution – testing boundary conditions7.Intertemporal ChoiceC. Manipulations of Utility Functions1.Properties of the Indirect Utility/Expenditure Functions2.Finding the expenditure function from indirect utility3.Finding Hicksian/Marshallian Demand from indirect utility/expenditure4.Recovering one Hicksian Demand from another5.Moving from Marshallian Demand -> Hicksian Demand6.Constructing Utility functions from Indirect Utility7.Money Metric Utility Functions8.Properties of the Slutsky Matrix, properties of the symmetric matrix (Secondderivates of expenditure function)D. Choice1.Income and Substitution Effects2.Construction of the Slusky Matrix (With and Without Endowments)3.Inferior Goods, Giffen Goods4.WARP, GARP.5.Recovering preferences from choicesE. Aggregation1.Construction of Demand Curves2.Homothetic utility Functions (Form of expenditure function, properties of slutskymatrix)3.Aggregation across goods4.Gorman FormF. Uncertainty1.Properties necessary for vNM utility functions2.Affine Transformations3.Risk Aversion, Risk Neutral, Risk Loving4.Absolute, Relative risk aversion5.Certainty Equivalent6.Risk Premium7.Simple InsuranceII. Production 15-25% of testA. Technology1.Isoquants, Technical Rate of Substitution2.CRTS, DRTS, IRTS3.Production possibility frontier4.Short Run/Long Run ConstraintsB. Profit Maximization1.Setting up and solving profit maximization problems2.Testing for firm shut down3.WAPM4.Cost Minimization <-> Profit Maximization5.Factor Demands6.Supply FunctionC. Cost Minimization1.Techniques for minimizing costs2.Multiple Plant Problems3.Marginal Costs4.Sunk Costs5.Cost function, Conditional Factor DemandsUseful Diagrams:Consumer Thoery:SlutskyMatrix∂⎡∂∂⎡∂∂∂∂(Ordinal)Utility Maximization Expenditure Minimization (,)max ()x Marshallian Demand Function (,)(,):xiV p m U x p mx p m V p m =⋅=(,)min x st ()(,)e p u p U x ue p u =⋅>∂Monotonic Transformations 111221*********212212222(,)(,):(,)(,)(,)(,)(,)(,)(,)(,)(,)(,)Matrix Symmetry e p u e p u p p p p is Neg SemiDef e p u e p u p p p p h p u h p u e p u e p u p p p p p p e p u e p u h p u h p u p p p p p p ∂⎤⎢⎥∂∂∂∂⎢⎥∂∂⎢⎥⎢⎥∂∂∂∂⎣⎦∂∂⎤⎢⎥∂∂∂∂∂∂⎢⎥=∂∂∂∂⎢⎥⎢⎥∂∂∂∂∂∂⎣⎦11112(,)(,)(,)0,h p u h p u h p u p p p ⎡⎤⎢⎥∂⎢⎥→≤=⎢⎥∂⎢⎥⎣⎦2,)(,,im q q m μ)m=Producer Thoery:Conditional Demand Function Y=f(x)Profit MaximizationWe can do something similar to WAPM here. Notice that for a firm to Cost MinimizationProfit Function (,)max ()Input Demand Function (,)Supply Function (,)x p w pf x wx x p w y p w π=−Cost Function c(,)min :()(,)x w y wx SubjectTo f x yx w y ==y max (,)Solve py c w y −y profit maximize (p,w)= max (,).Since for any p,w we know y and (p,w), we can reconstruct c(w,y) from the points.py c w y ππ−。

MIT英文版线性代数试卷(1)

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(b) What is the column space of A? Describe the nullspace of A.
Solution:
The column space is a 3-dimensional space inside a 3-dimensional space , i.e.
18.06 Linear Algebra
Spring 2010
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21年考研真题英语答案

21年考研真题英语答案来自21年考研真题的英语部分，本文将提供详细的答案解析以帮助考生更好地理解和准备考试。

以下将按照题目的顺序给出解答，并提供相关的解题思路和对答案的详细解析。

阅读理解部分：Passage 1:1. A解析：根据第一段的句子"Physicists have identified the source of "tricritical” magnetic behavior in a material that could benefit next-generation computing." 可知，物理学家已经找到了下一代计算机中受益的材料的“三重临界”磁性行为的来源。

根据上下文也可以判断出这是一项新的发现。

2. C解析：根据第三段 "This is the first time that a new type of magnetic behavior has been predicted theoretically and then discovered experimentally." 可知，从理论上预测然后通过实验证明这种新型磁性行为是第一次。

所以选C。

3. B解析：根据第六段 "These are intriguing discoveries that will help unlock novel electric and magnetic effects." 可知，这些都是令人感兴趣的发现，将有助于揭示新的电磁效应。

4. D解析：根据最后一段的最后一句 "The effort could also create a path to finding other novel materials with potentially useful properties." 可知，此举还可以为发现其他具有潜在有用性能的新材料铺平道路。

MIT量子物理exam

i A.Physical Constants and Conversion Factors Quantity Symbol Value UnitsAtomic mass unit amu931.5MeV/c21.661×10−27kgElectron mass m e0.511MeV/c29.109×10−31kgElementary charge e1.602×10−19C4.803×10−10esuPlanck’s constant h4.136×10−15eV s6.626×10−27erg s¯h=h/(2π)6.583×10−16eV s1.054×10−27erg sSpeed of light in vacuum c2.998×1010cm/s1eV=1.602×10−12erg1˚A=10−8cmhc=1.240×104eV˚A¯h c=1.973×103eV˚AB.Selected FormulaeEinstein-Planck relation:E=hν(1)DeBroglie relation:λ=hp(2)Rutherford scattering formula:dσdΩ=qQ2mv2◦21sin4(θ/2)(3)Radius of allowed orbits in Bohr model of hydrogenic atom:r n=n2Za0(4)wherea0=¯h2e2m(Bohr radius)(5)Solid angle of thin ring of width dθat angleθ(polar coordinates):dΩ=2πsinθdθ(6)11.Short Problems.(30points)(a).Davisson-Germer experiment(6points)A beam of electrons with kinetic energy K is scattered from a sin-gle crystal of nickel.A peak is observed in the diﬀraction pattern which is consistent with Bragg scattering of particles with wavelength λ=2.0˚A.What is the kinetic energy K(in units of eV)of the incident electrons?(b).Rutherford scattering(7points).In the Rutherford scattering ex-periment,a beam ofα-particles impinges upon a thin gold foil.Sig-niﬁcant scattering is observed at large angles(some particles are even backscattered atθ=180◦).Find the ratio of the rate of particles that scatter into a thin ring of thickness dθatθ=100◦to those that scatter into a thin ring of thickness dθatθ=50◦.(c).Photoelectric eﬀect(7points).As a result of shining monochromaticlight with wavelength800˚A on a metal surface,electrons are ejected which have a maximum kinetic energy of2eV.What is the maximum wavelength of light that can eject electrons from this metal surface?Compute the numerical value of this wavelength in angstroms(˚A).(d).Muonic atom(10points).The negative muon is a particle with thesame charge as the electron but with a larger mass(m=207m e).It is possible for the muon to be captured into orbits around the nuclei of atoms in a material and form a“muonic atom.”The inner orbit of the muon lies much closer to the nucleus than that of any electron.(i)(5points)Suppose the muon orbits a copper nucleus(Z=29).Find the radius of the innermost muonic orbit.Express your an-swer in units of a0(the Bohr radius for hydrogen).(ii)(5points)For copper,the energy of the n=2→n=1muonic transition is measured to be signiﬁcantly lower than one wouldcalculate for a point nucleus.Explain brieﬂy what this indicatesabout the radius of the copper nucleus.22.Bohr model for power law potential(30points)A particle of mass m moves in a central potential given byV(r)=V0 rak.(a).(16points)Use the Bohr quantization condition for angular momen-tum,L=n¯h,to calculate the quantized energies of allowed orbits of the particle.(Your answer should show the dependence on the quantum number n).(b).(7points)What value of k corresponds to the hydrogen atom?Findvalues for V0and a(or a suitable combination of these constants)which give the correct potential for hydrogen.(c).(7points)Use your result from parts a)and b)to calculate the energylevels of the hydrogen atom.33.Heisenberg Uncertainty Principle(20points)(a).(10points)A collimated stream of particles of mass m and charge qare accelerated from rest through a voltage V.They fall upon a slit of width d.What is the approximate angular divergence of the beam emerging from the other side?(b).(10points)Monochromatic light with wavelength of6000˚A passesthrough a fast shutter that opens for10−9sec.What is the approximate spread of wavelengths∆λof the light after it has passed through the shutter?4 4.Square wave function.(20points)The state of a free particle at t=0is described by the following wavefunction:Ψ(x,0)=⎧⎪⎨⎪⎩0x<−bA−b≤x≤3b 0x>3b.(a).(5points)Find A using the normalization condition.(You may choosethe phase convention such that A is real.)(b).(5points)What is the probability ofﬁnding the particle within theinterval x∈[0,b]at time t=0?(c).(10points)Calculate x and x2 for this state.。

2021年研究生英语模拟试卷与答案解析1

3.The storage vessel has a（）of 10,000 liters.
A：capacity
B：capability
C：ability
D：faculty
【答案】：A
【解析】：capacity指生产能力或容纳能力。B.capability用于人指智力方面的潜在能力，用于物指可能性或适应性；C.ability指人可通过学习来获得做好事的能力；D.faculty指人在某方面的特殊能力。
A：favorable to
B：interested in
C：hostile to
D：conscious of
【答案】：C
【解析】：词组辨析题。A.favorable to赞成;B.interested in对……感兴趣;C.hostile to敌对;D.conscious of意识到。本题上文出现大量负面词汇,如fear,reduce等。本句没有出现任何转折词汇,说明本句与上文关系为并列或递进,故该空也应填人负面词汇,从而使上下文正负色彩一致。选项中A.为正向词汇,B.D.偏向中性,唯有C.为负面词汇,故C.为答案。
2021年研究生英语模拟试卷与答案解析1
一、单选题(共40题)
1.Most of us have experienced the odd feeling of deja vu,often regarded as a supernatural force or a glitch in the matrix.You may perform an action and suddenly feel as though you have done it in that exact l manner sometime in your life.The feeling may even be 2 by a place or by spoken words,leaving some with the feeling they could 3 0r predict what happens next.Deja vu usually strikes without 4.But researchers from Colorado State University（CSU）have developed a technique to induce thes,6 previous experiment methods.Participants were led through virtual reality scenes 7 a junkyard or a hedge garden,which shared slight spatial similarities 8 were thematically unrelated.9 they could not"consciously remember the prior scene,"one researcher said,the participants'brain picked up on it and recognized"the similarity."The results showed deja vu"did not 10 above-chance ability to predict the next turn in a navigational path resembling a（n）11 experienced but unrecalled path,"although participants did report"12 feelings of knowing the direction of the next turn."Researchers 13 dejavu does not predict the future but makes people believe they can.It has been 14 as a"metamemory"phenomena,reflectinga（n）15 awareness of unspecific memories.Follow-up experiments are now being 16 by the team to look（）the main cause behind the feeling of prediction.The studies hope to address 18 it's the familiarity process that 19 the feeling,or hindsight bias 20 people feel convinced they knew what was going to happen after it happens

2021研究生英语作文题目

2021研究生英语作文题目The Importance of Critical Thinking in Graduate Studies。

Introduction。

Critical thinking is an essential skill that plays a crucial role in graduate studies. It enables students to analyze information, evaluate arguments, and make informed decisions. In today's complex and rapidly changing world, the ability to think critically is more important than ever. This article discusses the significance of critical thinking in graduate studies and provides strategies for developing this skill.Body。

1. Enhancing Analytical Skills。

Critical thinking enhances students' analytical skills, enabling them to break down complex problems into smaller, more manageable parts. By analyzing information from different perspectives, students can identify patterns, connections, and underlying assumptions. This analytical approach allows them to gain a deeper understanding of the subject matter and develop well-reasoned arguments.2. Promoting Effective Communication。

第二届哈佛大学-麻省理工数学竞赛代数题及解答

Harvard Math TournamentFebruary 27, 19991. If a@b = , for how many real values of a does a@1 = 0?2. For what single digit n does 91 divide the 9-digit number 12345n789?3. Alex is stuck on a platform ﬂoating over an abyss at 1 ft/s. An evil physicist has arranged for the platform to fall in (taking Alex with it) after traveling 100ft. One minute after the platform was launched, Edward arrives with a second platform capable of ﬂoating all the way across the abyss. He calculates for 5 seconds, then launches the second platform in such a way as to maximize the time that one end of Alex’s platform is between the two ends of the new platform, thus giving Alex as much time as possible to switch. If both platforms are 5 ft long and move with constant velocity once launched, what is the speed of the second platform (in ft/s)?4. Find all possible values of d where a2 6ad + 8d2 = 0, a = 0.5. You are trapped in a room with only one exit, a long hallway with a series of doors and land mines. To get out you must open all the doors and disarm all the mines. In the room is a panel with 3 buttons, which conveniently contains an instruction manual. The red button arms a mine, the yellow button disarms two mines and closes a door, and the green button opens two doors. Initially 3 doors are closed and 3 mines are armed. The manual warns that attempting to disarm two mines or open two doors when only one is armed/closed will reset the system to its initial state. What is the minimum number of buttons you must push to get out?6. Carl and Bob can demolish a building in 6 days, Anne and Bob can do it in 3, Anne and Carl in 5. How many days does it take all of them working together if Carl gets injured at the end of the rst day and can’t come back? Express your answer as a fraction in lowest terms.7. Matt has somewhere between 1000 and 2000 pieces of paper he’s trying to divide into piles of the same size (but not all in one pile or piles of one sheet each). He tries 2, 3, 4, 5, 6, 7, and 8 piles but ends up with one sheet left over each time. How many piles does he need?8. If f (x) is a monic quartic polynomial such that f ( 1) = 1, f (2) = 4, f ( 3) = 9, andf (4) = 16, nd f (1).9. How many ways are there to cover a 3 × 8 rectangle with 12 identical dominoes?10. Pyramid EARLY is placed in (x y z) coordinates so that E = (10 10 0), A = (10 10 0), R = ( 10 10 0), L = ( 10 10 0), and Y = (0 0 10). Tunnels are drilled through the pyramid in such a way that one can move from (x y z) to any of the 9 points (x y z 1), (x ± 1 y z 1), (x y ± 1 z 1),(x ± 1 y ± 1 z 1). Sean starts at Y and moves randomly down to the base of thepyramid, choosing each of the possible paths with probabilityeach time. What is the probability9that he ends up at the point (8 9 0)?1Algebra SolutionsHarvard-MIT Math TournamentFebruary 27, 1999Problem A1 [3 points]If a@b = a a 3b 3 , for how many real values of a does a@1 = 0?e S x o t l r u a t neo ion:us If ss ,in 0c e t h th en a t a ma k e 1s ,he 0 d o e r n 2o f +th a o g in =a l 0 .ex pres Thus si o a n 1,o r a wh i is c h a i r s oo a t nof a 2 + a + 1. But this quadratic has no real roots, in particular its roots are − 1±2√−3 . Thereforethere are no such real values of a, so the answer is 0.Problem A2 [3 points]For what single digit n does 91 divide the 9-digit number 12345n789?Solution 1: 123450789 leaves a remainder of 7 when divided by 91, and 1000 leaves a remainder of 90, or -1, so adding 7 multiples of 1000 will give us a multiple of 91.Solution 2: For those who don’t like long division, there is a quicker way. First notice that 91 = 7 13, and 7 11 13 = 1001. Observe that 12345n789 = 123 1001000+45 n 1001 123 1001+123 45n+789 It follows that 91 will divide 12345n789 i ﬀ 91 divides 123 45n + 789 = 462n. The number 462 is divisible by 7 and leaves a remainder of 7 when divided by 13.Problem A3 [4 points]Alex is stuck on a platform ﬂoating over an abyss at 1 ft/s. An evil physicist has arranged for the platform to fall in (taking Alex with it) after traveling 100ft. One minute after the platform was launched, Edward arrives with a second platform capable of ﬂoating all the way across the abyss. He calculates for 5 seconds, then launches the second platform in such a way as to maximize the time that one end of Alex’s platform is between the two ends of the new platform, thus giving Alex as much time as possible to switch. If both platforms are 5 ft long and move with constant velocity once launched, what is the speed of the second platform (in ft/s)?Solution: The slower the second platform is moving, the longer it will stay next to the ﬁrst platform. However, it needs to be moving fast enough to reach the ﬁrst platform before it’s too late. Let v be the velocity of the second platform. It starts 65 feet behind the ﬁrst platform, so it reaches the s．i pdel edhhlines up with the front of the ﬁrst platform at the instant that the ﬁrst platform has travelled 100ft, which occurs after 100 seconds. Since the second platform is launched 65 seconds later and has to travel 105 feet, its speed is 105/35 = 3ft/s.12Find all possible values of a dwhere a 2 − 6ad + 8d 2 = 0, a = 0. Solution: Dividing a 2 − 6ad + 8d 2 = 0 by a 2 , we get 1 − 6a d + 8(ad )2 = 0. The roots of this quadratic are 21 , 41 .Problem A5 [5 points]You are trapped in a room with only one exit, a long hallway with a series of doors and land mines. To get out you must open all the doors and disarm all the mines. In the room is a panel with 3 buttons, which conveniently contains an instruction manual. The red button arms a mine, the yellow button disarms two mines and closes a door, and the green button opens two doors. Initially 3 doors are closed and 3 mines are armed. The manual warns that attempting to disarm two mines or open two doors when only one is armed/closed will reset the system to its initial state. What is the minimum number of buttons you must push to get out?Solution: Clearly we do not want to reset the system at any time. After pressing the red button r times, the yellow button y times, and the green button g times, there will be 3 + r − 2y armed mines and 3 + y − 2g closed doors, so we want the values of r , y , and g that make both of these quantities 0 while minimizing r + y + g. From the number of doors we see that y must be odd, from the number of mines we see y = (3 + r)/2 ≥ 3/2, so y ≥ 3. Then g = (3 + y)/2 ≥ 3, and r = 2y − 3 ≥ 3, so r + y + g ≥ 9. Call the red, yellow, and green buttons 1, 2, and 3 respectively for notational convenience, then a sequence of buttons that would get you out is 123123123. Another possibility is 111222333, and of course there are others. Therefore the answer is 9.Problem A6 [5 points]Carl and Bob can demolish a building in 6 days, Anne and Bob can do it in 3, Anne and Carl in5. How many days does it take all of them working together if Carl gets injured at the end of the ﬁrst day and can’t come back? Express your answer as a fraction in lowest terms.Solution: Let a be the portion of the work that Anne does in one day, similarly b for Bob and c for Carl. Then what we are given is the system of equations b + c = 1/6, a + b = 1/3, and a + c = 1/5. Thus in the ﬁrst day they complete a + b + c = 21(1/6 + 1/3 + 1/5) = 7/20, leaving 13/20 for Anne and Bob to complete. This takes 113//320= 39/20 days, for a total of 2059 .Matt has somewhere between 1000 and 2000 pieces of paper he’s trying to divide into piles of the same size (but not all in one pile or piles of one sheet each). He tries 2, 3, 4, 5, 6, 7, and 8 piles but ends up with one sheet left over each time. How many piles does he need?Solution: The number of sheets will leave a remainder of 1 when divided by the least common multiple of 2, 3, 4, 5, 6, 7, and 8, which is 8 · 3 · 5 · 7 = 840. Since the number of sheets is between 1000 and 2000, the only possibility is 1681. The number of piles must be a divisor of 1681 = 412 , hence it must be 41.23If f (x) is a monic quartic polynomial such that f (−1) = −1, f (2) = −4, f (−3) = −9, and f (4) = −16, ﬁnd f (1).Solution: The given data tells us that the roots of f (x) + x 2 are -1, 2, -3, and 4. Combining with the fact that f is monic and quartic we get f (x) + x 2 = (x + 1)(x − 2)(x + 3)(x − 4). Hence f (1) = (2)(−1)(4)(−3) − 1 = 23.Problem A9 [7 points]How many ways are there to cover a 3 × 8 rectangle with 12 identical dominoes?Solution: Trivially there is 1 way to tile a 3 × 0 rectangle, and it is not hard to see there are 3 waysto tile a 3 × 2. Let T n be the number of tilings of a 3 × n rectangle, where n is even. From the diagram below we see the recursion T n = 3T n −2 + 2(T n −4 + T n −6 + . . . + T 2 + T 0). Given that, we can just calculate T 4 = 11, T 6 = 41, and T 8 is 153.Problem A10 [8 points]Pyramid EARLY is placed in (x,y , z) coordinates so that E = (10, 10, 0), A = (10, −10, 0), R = (−10, −10, 0), L = (−10, 10, 0), and Y = (0, 0, 10). Tunnels are drilled through the pyramid in such a way that one can move from (x,y , z) to any of the 9 points (x,y , z − 1), (x ± 1, y , z − 1), (x, y ± 1, z − 1),(x ± 1, y ± 1, z − 1). Sean starts at Y and moves randomly down to the base of the pyramid, choosing each of the possible paths with probability 91each time. What is the probability that he ends up at the point (8, 9, 0)?. . . . . . etc...Solution 1: Start by ﬁguring out the probabilities of ending up at each point on the way down the pyramid. Obviously we start at the top vertex with probability 1, and each point on the next level down with probability 1/9. Since each probability after n steps will be some integer over 9n, we will look only at those numerators. The third level down has probabilities as shown below. Think of this as what you would see if you looked at the pyramid from above, and peeled oﬀthe top two layers.1 2 3 2 1246423 6 9 6 3246421 2 3 2 134What we can observe here is not only the symmetry along vertical, horizontal, and diagonal axes, but also that each number is the product of the numbers at the ends of its row and column (e.g. 6 = 2 · 3). This comes from the notion of independence of events, i.e. that if we east and then south, we end up in the same place as if we had moved south and then east. Since we are only looking for the probability of ending up at (8, 9, 0), we need only know that this is true for the top two rows of the square of probabilities, which depend only on the top two rows of the previous layer. This will follow from the calculation of the top row of each square, which we can do via an algorithm similar to Pascal’s triangle. In the diagram below, each element is the sum of the 3 above it.11 1 11 2 3 2 11 3 6 7 6 3 11 4 10 16 19 16 10 4 11 5 15 30 45 51 45 30 15 5 1Now observe that the ﬁrst 3 numbers in row n , where the top is row 0, are 1, n , n (n2+1) . This factis easily proved by induction on n , so the details are left to the reader. Now we can calculate the top two rows of each square via another induction argument, or by independence, to establish that the second row is always n times the ﬁrst row. Therefore the probability of ending up at the point (8,9,0) is 910550 .Solution 2: At each move, the ① and y coordinates can each increase by 1, decrease by 1, or stay the same. The y coordinate must increase 9 times and stay the same 1 times, the ① coordinate can either increase 8 times and stay the same 1 time or decrease 1 time and increase 9 times. Now we consider every possible case. First consider the cases where the ① coordinate decreases once. If the ① coordinate decreases while the y coordinate increases, then we have 8 moves that are the sameand 2 that are di ﬀerent, which can be done in 8!10! = 90 ways. If the ① coordinate decreases whilethe y coordinate stays the same, then we have 9 moves that are the same and 1 other, which can bedone in 9!10! = 10 ways. Now consider the cases where the ① coordinate stays the same twice. If the y coordinate stays the same while the ① coordinate increases, then we have 7 moves that are thesame, 2 that are the same, and 1 other, which can be done in 71!20!!= 360 ways. If the y coordinate stays the same while the ① coordinate stays the same, then we have 8 moves that are the same and 24 that are di ﬀerent, which can be done in 8!10! = 90 ways. Therefore there are 360 + 90 + 90 + 10 = 550paths to (8,9,0), out of 91 0 possible paths to the bottom, so the probability of ending up at the point (8,9,0) is 910550 .。

2021英语考研真题作文

2021英语考研真题作文It is undeniable that the English postgraduate entrance examination (commonly known as the English exam) is an extremely important test for many students in China. As the competition becomes increasingly fierce, it is crucial for candidates to be well-prepared in order to achieve satisfactory results. In this essay, we will explore some effective strategies and tips for tackling the English exam.First and foremost, it is essential to have a comprehensive understanding of the exam structure. The English exam typically consists of two sections: writing and translation. For the writing section, candidates are required to write an essay in response to a given topic, while the translation section tests the ability to translate English passages into Chinese. Familiarize yourself with the expectations and requirements of each section can help you better allocate your time and energy during the preparation phase.To excel in the writing section, it is of utmost importance to enhance your writing skills. Regular reading, both in English and in Chinese, can greatly contribute to expanding your vocabulary and improving your sentence structure. Additionally, practice writing essays on various topics to hone your ability to express ideas clearly and coherently. Take advantage of online resources and engage in peer evaluations to receive feedback and make necessary improvements.In terms of the translation section, it is crucial to practice translating English texts into Chinese on a regular basis. Focus on improving the accuracy and fidelity of your translations, as well as mastering the appropriate use of idiomatic expressions. It is also beneficial to compareyour translations with professional translations to identify areas for further improvement. Keep in mind that consistent practice and exposure to various types of texts will help you become more familiar with the different styles and nuances of translation.Aside from individual preparation, participating in mock exams can greatly enhance your confidence and test-taking skills. Mock exams simulate the actual exam environment, which allows you to familiarize yourself with the time constraints and alleviate test anxiety. Analyze your performance in each mock exam and identify areas that need further improvement. By repeatedly putting yourself in a test-like situation, you can progressively refine your strategies and enhance your overall performance.Furthermore, effective time management is crucial during the actual exam. Allocate enough time for both the writing and translation sections, as well as leave some buffer time for proofreading and revision. It is advisable to read through the prompts or questions carefully before starting, as thiswill help you formulate a clear plan and allocate your time accordingly. Stick to your plan and avoid spending too much time on any single question. Remember, time is limited, so staying focused and organized is key to completing the exam within the given timeframe.In conclusion, the English exam is a significant hurdle for many students. By understanding the exam structure, improving writing and translation skills, participating in mock exams, and managing time effectively, candidates can greatly increase their chances of success. With diligent preparation and a focused mindset, success in the English exam is within reach. Good luck to all the candidates!。

21年英语一38题

21年英语一38题In recent years, the issue of artificial intelligence (AI) has become increasingly prevalent in our lives. People are both fascinated and concerned about the rapid development and integration of AI technology. The 38th question of the 2021 English exam for college entrance exams in China explores the topic of AI and its impact on employment. This question requires us to analyze the relationship between AI and employment and provide our own insights.AI technology has made remarkable progress and is being applied in various industries, including manufacturing, healthcare, finance, and customer service. While AI brings numerous benefits and efficiency, there is also a growing concern about its impact on the job market. Some people believe that AI will inevitably replace human workers, leading to a significant loss of employment opportunities. However, a more comprehensive understanding of the issue reveals a more complex and nuanced picture.Firstly, it is undeniable that AI has the potential to automate certain repetitive and mundane tasks. For example, in manufacturing industries, AI-powered robots can perform assembly line work more efficiently and accurately than human workers. This may result in a decrease in the demand for certain low-skilled jobs. However, the introduction of AI technology also creates new job opportunities in the field of AI research, development, and maintenance. These high-skilled positions require expertise and knowledge that are in demand in the AI-driven economy.Secondly, AI technology is not only about replacing human workers but also about augmenting human capabilities. AI can assist and enhance human performance, enabling workers to focus on more complex and creative tasks. For instance, in the healthcare sector, AI algorithms can analyze medical data and provide accurate diagnoses, freeing up doctors' time to focus on patient care and treatment. This symbiotic relationship between AI and human workers can lead to increased productivity and job satisfaction.Moreover, AI technology is constantly evolving, and its impact on the job market is not fixed or uniform. While some jobs may be displaced by AI, new job opportunitieswill also emerge. The key lies in adapting and upskilling the workforce to meet the demands of the evolving job market. Governments and educational institutions should play a crucial role in providing training programs and resources to equip workers with the necessary skills to thrive in the AI era. Lifelong learning and reskilling initiatives are essential to ensure that workers can transition into new roles and industries.In conclusion, the relationship between AI and employment is multifaceted. While AI technology has the potential to automate certain tasks, it also creates new job opportunities and enhances human capabilities. The impact of AI on the job market is not fixed and depends on various factors, including the adaptability of the workforce and the implementation of effective policies. To harness the benefits of AI and mitigate potential negative impacts, it is essential to foster a balanced and proactive approach that embraces innovation while also investing in human capital. By doing so, we can ensure a prosperous future where AI and human workers can thrive together.。

mit高数试题

MIT OpenCourseWare
18.01 Single Variable Calculus
Fall 2006
For information about citing these materials or our Terms of Use, visit: /terms.
Notation: 2.1 = Section 2.1 of the Simmons book; Notes G = section G of the Notes; 1A-3 = Exercise 1A-3 in Section E (Exercises) of the Notes (solved in section S) 2.4/13; 81/4 = in Simmons, respectively, section 2.4 Problem 13; page 81 Problem 4 Recitation 0. Wed. Sept. 6 Graphing functions. Read: Notes G, sections 1-4 Work: 1A-1a, 2a, 3abe, 6a, 7a Lecture 1. Thurs., Sept. 7 Derivative; slope, velocity, rate of change. Read: 2.1-2.4 Work: 1C-3abe, 4ab (use 3), 5, 6 (trace axes onto your answer sheet) Work: 1B-2, 1C-1a (start from the deﬁnition of derivative) Lecture 2. Fri. Sept. 8 Limits and continuity; some trigonometric limits Read: 2.5 (bottom p.70-73; concentrate on examples, skip the � − δ def’n) Read: 2.6 to p. 75; learn def’n (1) and proof “diﬀerentiable =⇒ continuous” at the end. Read: Notes C Work: 1D-1bcefg, 4a; 1C-2, 1D-3ade, 6a, 8a (hint: “diﬀ =⇒ cont.”) Lecture 3. Tues. Sept. 12 Diﬀerentiation formulas: products and quotients; Derivatives of trigonometric functions.

MIT数学分析考试试题1

∞ � 1 cos(nx) 3 n n=1
deﬁnes a continuously diﬀerentiable function on the real line. Solution. Since | cos(nx)| ≤ 1, and the series
∞ � n=11 1 n3
converges,
1
2
18.100B, FALL 2002 FINAL EXAM: DECEMBER 16
By a theorem in Rudin, a real-valued continuous function on a compact metric space, such as [0, 1] has a minimum. � Comment: Generally well done, as it should have been. Problem 4 Let f : R −→ R be twice diﬀerentiable and suppose that 0 is a local maximum of f, i.e. for some > 0 f (x) ≤ f (0) for all x ∈ (− , ). Show that f (0) ≤ 0. Solution. We know from class that f (0) = 0 since 0 is a local maximum – in any case this follows that the diﬀerence quotient (f (x) − f (0))/x is ≥ 0 for x ∈ (− , 0) and ≤ 0 for x ∈ (0, ). By the mean value theorem for each n, large, there is a point cn ∈ (−1/n, 0) such that f (x) − f (0) = xf (cn ), so f (cn ) ≥ 0. Since f is diﬀerentiable we must have f (cn )/cn → f (0) as n → ∞ which shows that f (0) ≤ 0. � Comment: Alternatively one can assume that f (0) > 0 and arrive at a contradiction. However, one cannot assume that f (x) > 0 for x near 0, since I did not say that f is continuous – this lead many people into error. Similarly you cannot just assume that f (x) ≥ 0 for x ∈ (−δ, 0) and small enough δ. It is simply not true in general. Problem 5 If g : R −→ R is a diﬀerentiable function and g is bounded on R, show that g is uniformly continuous. Solution. By assumption, there exists M ∈ R such that |g (x)| < M for all x ∈ R. By the Mean Value Theorem, if x < y ∈ R there exists c ∈ (x, y ) such that g (y ) − g (x) = g (c)(y − x). It follows that |g (y ) − g (x)| ≤ M |x − y | since this is true whe x = y, and for x = y, exchanging x and y as necessary. Thus, given > 0 choosing δ < /M, |g (y ) − g (x)| < whenever |y − x| < δ and this is the deﬁnition of uniform continuity. � Comment: Arguments involving the integration of g received few marks, since it is not assumed that g is integrable. Claims that the diﬀerence quotients were uniformly bounded without appeal to the MVT were not successful. Problem 6 Using standard properties of the cosine function explain why the formula f (x) =

2021年物理系各专业研究生入学考试《量子力学》试验型考试试题(试卷A)

XXX大学
2021年物理系各专业研究生入学考试
《量子力学》实验型考试试题（试卷E）
1、对于氢原子的结构，采用电子绕核做圆周运动的半经典模型：
（1）从德布罗意（驻）波的观点导出波尔关于定态轨道的量子化条件。

（2）从牛顿定律和（1）的量子化条件导出氢原子的轨道半径和能量。

2、一个质量为μ的粒子，处于势阱：
()0V x ∞⎧⎪=⎨⎪∞⎩
00x x a x a <≤≤>中，
0t =时，其归一化波函数为：
(
),014cos sin ,x t x x a a ππψ⎫==-⎪⎭
求：（1）后来某时刻0t t =时的波函数。

（2）在0t =和0t t =时体系的平均能量。

3、设ˆF
为厄密算符，证明在能量表象中下式成立： ()21ˆˆˆ,,2
n k nk n E E F k F H F k ⎡⎤⎡⎤-=
⎣⎦⎣⎦∑
4、设钠原子（原子序数为11）处于沿Z 方向的强磁场中：
（1）计入自旋（但不计旋轨耦合），写出其价电子的哈密顿量（只计入B 的一次项），并写出相应定态能量和波函数的通式（主要标志出对量子数和空间坐标的依赖性）。

（2）说明此情形下钠原子发射光谱中黄线的塞曼分裂现象。

5、设质量为m ，电荷为q 的粒子被约束在谐振子势()212V x kx =内。

现沿x 方向加上一个恒定的电场ε，试计算其基态0和第一激发态1的能级移动，准确到二级。

提示：已知如下矩阵元通式：
,1,12m n m n n m x n m δω-+⎡⎤=+⎢⎥⎦。

难度大一点的试题及答案

难度大一点的试题及答案1. 问题：请解释量子纠缠现象，并讨论其在量子计算中的应用。

答案：量子纠缠是量子力学中的一种现象，其中两个或多个粒子的量子态以一种方式相互关联，以至于一个粒子的状态立即影响另一个粒子的状态，无论它们相隔多远。

这种现象违反了经典物理学中的局域性原理，即物理效应不能瞬间跨越空间。

在量子计算中，量子纠缠是实现量子比特（qubits）之间信息共享的关键机制。

量子比特可以通过纠缠态来执行复杂的计算任务，如量子算法中的量子叠加和量子门操作。

量子纠缠使得量子计算机能够在处理大量数据时实现更高的计算速度和效率。

2. 问题：简述相对论中的时间膨胀效应，并给出一个实际应用的例子。

答案：时间膨胀是爱因斯坦相对论中的一个概念，它表明当一个物体以接近光速的速度运动时，相对于静止观察者来说，该物体上的时间流逝会变慢。

这意味着，对于高速运动的物体来说，时间似乎“膨胀”了。

一个实际应用的例子是全球定位系统（GPS）。

GPS卫星以高速绕地球运行，因此它们经历的时间膨胀效应。

为了确保地面接收器能够准确计算位置，GPS系统必须考虑这种时间膨胀效应，否则会导致定位误差。

3. 问题：描述DNA复制过程中的半保留复制机制，并解释其重要性。

答案：在DNA复制过程中，半保留复制机制是指每个新合成的DNA分子都包含一条原始的亲本链和一条新合成的子代链。

这种机制保证了遗传信息的准确传递，因为每个子代DNA分子都包含了完整的遗传信息。

半保留复制的重要性在于它确保了遗传信息的忠实复制和传递。

在细胞分裂时，每个新细胞都能获得一套完整的遗传信息，这对于生物体的生长、发育和遗传至关重要。

4. 问题：解释什么是费米能级，并讨论其在固体物理学中的作用。

答案：费米能级是固体物理学中的一个概念，指的是在绝对零度时，电子填充能带的最高能量状态。

费米能级是金属和半导体中电子分布的一个关键参数，它决定了材料的导电性。

在固体物理学中，费米能级对于理解材料的电子行为至关重要。

学历类《研究生考试》工程硕士《逻辑推理能力测试》考试试题及答案解析

学历类《研究生考试》工程硕士《逻辑推理能力测试》考试试题及答案解析姓名:_____________ 年级:____________ 学号:______________1、专家：只有当一个物品的产权界定清晰，并且能够对它进行交易时，该物品的真正价值才能体现出来。

我们说要保护农民的利益，如果连农民的最大利益是什么都搞不清楚，如何保护?农民有什么值钱的东西?就是那块宅基地。

只有让宅基地的价值得到充分体现，才叫真正保护农民的利益。

如果以上陈述为真，则以下哪项陈述必然为真?A、要想真正保护农民的利益，就要允许对宅基地进行交易。

B、只要搞清楚了什么是农民的最大利益，就能保护农民的利益。

C、只要宅基地的产权界定清晰，并且能够对它进行交易，它的真正价值就能体现出来。

D、如果对宅基地进行交易，它的价值就能够得到充分体现。

正确答案：C答案解析：暂无解析2、最近实施的一项历史上最严格的禁止吸烟的法律，虽然尚未禁止人们在其家中吸烟，却禁止人们在一切公共场所和工作地点吸烟。

如果这项法律得到严格执行，就会彻底保护上班人员免受二手烟的伤害。

如果以下哪项陈述为真，最有力地削弱了上述论证?A、上下班的人员吸入的汽车尾气要比吸二手烟的危害大得多。

B、诸如家教、护工、小时工等人员都在雇主的家里上班。

C、任何一项立法及其实施都不能完全实现立法者的意图。

D、这项控制吸烟的法律过高地估计了吸二手烟的危害。

正确答案：B答案解析：暂无解析3、近年来中国制造的成本不断上升，美国波士顿咨询集团的调研数据显示，中国制造的成本己接近美国。

以美国为基准(100)，中国制造指数是96，也就是说，同样一件产品，在美国制造成本是1美元，在中国制造则需要0.96美元。

尽管中国的人力成本有所上升，但中国工人的收入明显低于美国同行业工人的收入。

如果以下哪项陈述为真，能够最好地解释上述看似矛盾的现象?A、中国大部分地区的物价水平低于美国的物价水平，B、由于中国人力成本上升，一些制造业开始将部分工厂转往印度或东南亚国家。