问答题设随机变量X与Y相互独立，且X～N(0，σ2)，Y～N(0，σ2)．求：

问答题设f(x)在[0,1]上二阶连续可导，且f'(0)=f'(1)。证明：存在ζ∈(0,1),使得

问答题设f(x)在(-a，a)(a＞0)内连续，且f"(0)=2．

问答题设α 1 ，α 2 ，…，α n 为n个线性无关的n维向量，且与向量β正交．证明：向量β为零向量．

问答题将二重积分化为累次积分(两种形式)，其中积分区域D给定如下：

问答题设x与y均大于0且x≠y，证明：

问答题设二次型矩阵A满足AB=0，其中．(Ⅰ)用正交变换化二次型xTAx为标准形，并写出所用正交变换；(Ⅱ)求(A-3E)6．

问答题讨论线性方程组当λ为何值时，(1)线性方程组有唯一解；(2)线性方程组有无穷多解；(3)线性方程组无解．

问答题已知矩阵可逆，A*是A的伴随矩阵，是A*的特征向量．(Ⅰ)求A*的特征值与特征向量；(Ⅱ)判断A*能否相似对角化，如能则求可逆矩阵P使P-1A*P=A，如不能则说明理由．

问答题矩阵，矩阵B=(kE+A)2，k为实数.

问答题已知，求y"．

问答题设X，Y相互独立，且X～N(1，2)，Y～N(0，1)，求Z=2X-Y+3的密度．

问答题已知4元齐次线性方程组的解全是4元方程(ii)x1+x2+x3=0的解，(Ⅰ)求a的值；(Ⅱ)求齐次方程组(i)的解；(Ⅲ)求齐次方程(ii)的解．

问答题设，讨论f(x)的单调性，凹凸性，拐点，水平渐近线．

问答题A，B为n阶矩阵且r(A)+r(B)＜n．证明：方程组AX=0与BX=0有公共的非零解．

问答题已知，求常数a．

问答题简述要约及其要件。

问答题求函数z=x 2 +2y 2 -2x+4y+1满足条件x-2y-6=0的极值．

问答题求由方程y=e (x+y) 确定的函数y=f(x)的二阶导数。

问答题In the early 1800s, groups of English workers wrecked machines that they felt threatened their jobs. (46) They were called "Luddites" after one of their leaders, a term that is now used for anyone who puts up resistance to new technologies. (47) The odd thing about nanotechnology's Luddites is that they have started resisting before the technology has really established itself. As people start to buy products involving nanotechnology, from odour-resistant shirts to window glass that repels dirt, they will realise that many of these new things are useful and harmless. And as awareness of nanotechnology grows, they will begin to understand that it covers a range of different ways of doing things, some of which carry some risk and others do not. As a result, the technology's detractors will probably become more nuanced in their complaints. Nanotechnology has the potential to cause an industrial upheaval, just as electricity did in its time. (48) Like electricity, though, it has so many and such diverse applications that it is unlikely to arrive in one huge wave, as nanotechnology's critics fear. Instead, there will be a series of smaller waves. (49) Many of the innovations the technology may bring are a long way off, leaving plenty of time to prepare. Nanotechnology, like any new discovery, offers both risks and rewards. There will undoubtedly be some need to control its exploitation to minimize the risks, but there are also strong arguments for allowing the unfettered pursuit of knowledge, without it, innovation cannot flourish. Twenty years ago, nobody could have foreseen that the invention of a new microscope would launch a remarkable new technology, perhaps a revolution. (50) Scientists should be allowed to work with as little hindrance as possible to gain a better understanding of the object of their study-however large or small.