问题 选择题

有三个命题:①垂直于同一个平面的两条直线平行;②过平面α的一条斜线l有且仅有一个平面与α垂直;③异面直线a、b不垂直,那么过a的任一个平面与b都不垂直。其中正确命题的个数为(   )

A.0

B.1

C.2

D.3

答案

答案:D

①垂直于同一个平面的两条直线平行,这是直线垂直平面的性质定理。

②过平面α的一条斜线l有且仅有一个平面与α垂直;

从斜线l有取一点M(M不是斜足),过点M可一直线l’垂直于平面α,显然直线l’l’确定的平面垂直于平面α。而这个平面与点M的位置无关,所以此类平面唯一。

③反设存在过a的一个平面与b不垂直,由线面垂直的定义可知b必垂直a,与已知矛盾。

所以三个命题都是正确,选择D。

阅读理解

We need to make better use of our resources. In developing countries we have more than enough, if we are less wasteful in our ways. Fortunately, we can improve. The challenge lies not so much with ‘technical fixes’ but with our approach to our world around us. In the recent past we were in a “Wild West” economy, supposing that there would always be enough resources. Now we know there are no new Earth to explore and exploit; one image to illustrate this is to think of Earth as a spaceship, where most materials have to be recycled. For us, “moving on” will be a case of leaving behind the throwaway society and advancing to a conserver society.

To qualify as citizens of a conserver society, we must change traditional attitudes and thinking. We need to recognize that there is not very often such a thing as “waste”, rather, there are materials which sometimes end up in the wrong place. The change has already begun. The European steel industry reuses scrap(废弃的)metal, resulting in an energy saving of up to 50% . Recycling a glass container saves only 18%; but, in parts of the United States, a citizen buying a bottle of soda or beer now pays a deposit against return of the empty bottle.

If all drink containers in the USA were to be reused, the annual saving would be 0.5 million tons glass, plus about 50 million barrels of oil used in production processes. In Japan, OPEC promoted an increase in recycling of raw materials from 16% to 48% in just five years. In Norway, the price of a new car includes a disposal cost element of about 100 dollars, redeemable(可换成现款的)when the junked car is turned in at an approved receiving center.

Major new businesses are trying to exploit waste chemicals and oil. The Chinese claim to reuse 2.5 million tons of scrap iron and at least one million tons of waste paper each year. In the main, the conserver society depends on the commitment of individuals. But they can be encouraged by government incentive(鼓励) and punishment, which should apply at least as strongly to industry and other commercial interests.

73  Which of the following best expresses the meaning of “a conserver society” in the second paragraph?

A. A wasteful society.

B. A society which thinks of  ways of recycling waste materials.

C. A society which keeps everything.

D. A society which saves electricity.

74  In the last paragraph, the author suggests governments _______.

A. depends on individuals to find ways of conserving energy.

B. find ways of encouraging those industries and individuals who conserve energy and of punishing those who don’t.

C. depend on companies to find ways of saving energy and rewarding workers

D. help establish businesses that will exploit waste materials

75  In this passage the author _______.

A. explains that meaning of the “Wild West” economy

B. tells us what recycled materials are.

C. teaches us how to recycle materials.

D. recommend a change in our use of resources strongly

单项选择题