问答题设，求可逆矩阵C．使得CTAC为对角阵．

问答题设相似于对角阵．求：

问答题设X的概率密度为且P{X≤1}=

问答题计算．

问答题{{B}}Directions:{{/B}} {{I}}Read the following text carefully and then translate the underlined segments into Chinese. Write your pieces of Chinese version in the proper space on your Answer Sheet Ⅱ{{/I}}{{U}}The potential of computers for increasing the control of organizations or society over their members and for invading the privacy of those members has caused considerable concern.{{/U}} The privacy issue has been raised most insistently with respect to the creation and maintenance of data files that assemble information about persons from a multitude of sources. Files of this kind would be highly valuable for many kinds of economic and social research, but they are bought at too high a price if they endanger human freedom or seriously enhance the opportunities of blackmailers. (2) {{U}}While such dangers should not be ignored, it should be noted that the lack of comprehensive data files has never before been the limiting barrier to the suppression of human freedom{{/U}}. Making the computer the villain in the invasion of privacy or encroachment on civil liberties simply diverts attention from the real dangers. Computer data banks can and must be given the highest degree of protection from abuse. (3) {{U}}But we must be careful, also, that we do not employ such crude methods of protection as to deprive our society of important data it needs to understand its own social processes and to analyze its problems{{/U}}. Perhaps the most important question of all about the computer is what it has done and will do to man's view of himself and his place in the universe. (4) {{U}}The most heated attacks on the computer are not focused on its possible economic effects, its presumed destruction of job satisfaction, or its threat to privacy and liberty, but upon the claim that it causes people to be viewed, and to view themselves, as 'machines'{{/U}}. What the computer and the progress in artificial intelligence challenge is an ethic that rests on man's apartness from the rest of nature. An alternative ethic, of course, views man as a part of nature, governed by natural law, subject to the forces of gravity and the demands of his body. (5) {{U}}The debate about artificial intelligence and the simulation of man's thinking is, in considerable part, a confrontation of these two views of man's place in the universe{{/U}}.

问答题建立下列不定积分的递推公式：

问答题将函数展开成x的幂级数，并求级数的和．