问答题(Ⅰ)求f的矩阵A；(Ⅱ)求f的秩；(Ⅲ)当f的秩为2时，求矩阵A的特征值及特征向量；(Ⅵ)当f的秩为2时，用正交变换化二次型为标准形，并求出相应的正交变换矩阵．

问答题设总体X服从参数为(θ＞0)的指数分布，又设X1，X2，…，Xn是来自总体X的简单随机样本，令，计算EnZ．

问答题计算二重积分其中D是由x轴，y轴与曲线所围成的区域；α＞0，b＞0．

问答题(46) History tells us that in ancient Babylon, the cradle of our civilization, the people tried to build a tower that would reach to heaven. But the tower became the tower of Babel, according to the Old Testament, when the people were suddenly caused to speak different languages. In modern New York City, a new tower, that of the United Nations Building, thrusts its shining mass skyward. (47) But the realization of the UN's aspirations—and with it the hopes of the peoples of the world—is threatened by our contemporary Babel: about three thousand different languages are spoken throughout the world today, without counting the various dialects that confound communication between peoples of the same land. In China, for example, hundreds of different dialects are spoken; people of some villages have trouble passing the time of day with the inhabitants of the next town. In the new African state of Ghana, five million people speak fifty different dialects. In India more than one hundred languages are spoken, of which only fourteen are recognized as official. To add to the confusion, as the old established empires are broken up and new states are formed, new official tongues spring up at an increasing rate. In a world made smaller by jet travel, man is still isolated from many of his neighbors by the Babel barrier of multiplying languages. Communication is blocked daily in scores of ways. Travelers find it difficult to know the peoples of other nations. Scientists are often unable to read and benefit from the work being carried on by men of science in other countries. (48) The aims of international trade, of world accord, of meetings between nations, are blocked at every turn; the work of scholars, technologists, and humanists is handicapped. Even in the shining new tower of the United Nations in New York, speeches and discussions have to be translated and printed in the five official UN language—English, French, Spanish, Russian and Chinese. Confusion, delay, suspicion, and hard feelings are the products of the diplomatic Babel. The chances for world unity are lessened if, in the literal sense of the phrase, we do not speak the same language. (49) We stand in dire need of a common tongue, a language that would cross national barriers, one simple enough to be universally learned by travelers, businessmen, government representatives, scholars, and even by children at school. Of course, this isn't a new idea. Just as everyone is against sin, so everyone is for a common language that would further communication between nations. (50) What with one thing and another—our natural state of drift as human beings, our rivalries, resentments, and jealousies as nations—we have up until now failed to take any action. I propose that we stop just talking about it, as Mark Twain said of the weather, and do something about it. We must make the concerted, massive effort it takes to reach agreement on the adoption of a single, common auxiliary tongue.

问答题计算三重积分其中Ω是由锥面x2+y2=z2与平面z=a(a＞0)围成的区域，如图所示．

问答题设总体X服从指数分布，概率密度为X1，X2，…，Xn为取自总体X的简单随机样本.(1)证明：仍服从指数分布；(2)求常数C使为θ的无偏估计；(3)指出Z与哪个更有效.

问答题已知A为三阶实对称矩阵，若存在正交矩阵Q，使QTAQ=Q-1AQ=，且A*α=α，其中α=(-1，-1，1)T，A*为A的伴随矩阵．(2)求二次型XT(A*)-1x的表达式，并确定其正负惯性指数．

问答题作变换u=tany，x=et，试将方程化为u关于t的方程．

问答题设X～U(0，2)，Y=X 2 ，求Y的概率密度函数．

问答题设f(x)为连续函数，Ω=(x，y，z)|x2+y2+z2≤t2，z≥0)，∑为Ω的表面，Dxy为Ω在xOy平面上的投影区域，L为Dxy的边界曲线，当t＞0时有

问答题证明：在右半平面x＞0上，曲线积分与路径无关，求一个二元函数u=u(x，y)，使得。

问答题设a=(1，1，-1)T是的一个特征向量．