题目

Experts believe there are huge amounts of gas and oil in the Arctic. For some years, industries have looked at the ongoing Arctic ice melting as a source of possible profits from those natural resources. But researchers say methane (甲烷) gas will escape in amounts not seen before as the permafrost(永久冻土) melts. And that, scientists say, could cost the world trillions of dollars. Researchers from Britain’s University of Cambridge and the Netherlands’ Erasmus University Rotterdam looked at studies of methane gas releases in the East Siberian Sea. They thought that the releas12．如图，在平面直角坐标系中，边长为2的等边△CDE恰好与坐标系中的△OAB重合，现将△CDE绕边AB的中点G（G也是DE的中点），按顺时针方向旋转180°到△C′DE的位置．（1）求C′点的坐标；（2）求经过三点O、A、C′的抛物线的解析式；（3）如图③，⊙G是以AB为直径的圆，过B点作⊙G的切线与x轴交于点F，求切线BF的解析式；（4）在（3）的条件下，直线BF与抛物线交于M、N两点，P是MN上的动点，过P作x轴的垂线交抛物线于Q，求PQ的最大长度．