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问题 选择题
给出下列命题：
①如果函数f（x）对任意x∈R，都有f（a+x）=f（a-x）（a是常数），那么函数f（x）必是偶函数；
②如果函数f（x）对任意x∈R，都有f（2+x）=-f（x），那么函数f（x）是周期函数；
③如果函数f（x）对任意x1，x2∈R，且x1≠x2，都有
f(x1)-f(x2)
x1-x2
＞0，那么函数f（x）在R上是增函数；
④函数y=f（x）和函数y=f（x-1）+2的图象一定不会重合．
其中真命题的序号是（　　）
A．①④B．②③C．①②③D．②③④
答案

对于①而言，当a=1时，对称轴为x=1，故不是偶函数，则不正确，排除A和C

对比B与D，只需判定④的真假，当f（x）=2x时，函数y=f（x）和函数y=f（x-1）+2的图象重合，故不正确

故选B

解答题
已知向量
OP
=( 2cos(
π
2
+x) ， -1 )，
OQ
=( -sin(
π
2
-x) ， cos2x )，
定义f(x)=
OP
•
OQ

（1）求函数f（x）的表达式，并求其单调区间；
（2）在锐角△ABC中，角A、B、C对边分别为a、b、c，且f（A）=1，bc=8，求△ABC的面积、
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单项选择题

ICE


1Two conditions are necessary for the formation of ice: the presence of water and temperatures below freezing. Ice in the atmosphere and on the ground can assume various forms, depending on the conditions under which water is converted to its solid state~ Ice that forms in the atmosphere can fall to the ground as snow, sleet, or hail. Snow is an assemblage of ice crystals in the form of flakes; sleet is a collection of frozen raindrops, which are actually ice pellets. Hail consists of rounded or jagged lumps of ice, often in layers like the intemal structure of an onion. Ice also forms directly on the ground or on bodies of water. In North America, ice forms in late autumn, winter, and early spring. On very large bodies of water, it may not form until late winter because there must be several months of low temperatures to chill such large amounts of water.
2On puddles and small ponds, ice first freezes in a thin layer with definite crystal structure that becomes less apparent as the ice thickens. On lakes large enough to have waves, such as the Great Lakes, the first ice to form is a thin surface layer of slush, sometimes called grease ice, which eventually grows into small floes of pancake ice. If the lake is small enough or the weather cold enough, the floes may freeze together into a fairly solid sheet of pack ice. Pack ice may cover the entire lake or be restricted to areas near the shore.
3Because water expands when it freezes, ice is less dense than liquid water and therefore floats rather than sinks in water. As ice floats on the surface of a lake, ocean, or river, it acts as an insulator and is thus important in maintaining the balance of the ecosystem. Without the insulating effect of floating ice sheets, surface water would lose heat more rapidly, and large bodies of water such as the Arctic Ocean and Hudson Bay might freeze up completely.

Ice that forms in the atmosphere in the form of layered lumps is known as

A．snow

B．pack ice

C．hail

D．grease ice
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