Riddle time

Remember that Tetris game, with that delightful music copied from the Borat television show? Well in Tetris there are 7 different types of shapes: all the possible ways of combining four blocks (up to rotation, but not reflection). Is it possible to put all these 7 shapes together to form a rectangle? You must use each shape once and only once. Justify your answer, but make it as simple as possible.

Just use a checkerboard pattern. All pieces cover 2 black and 2 white blocks, except for the T piece (it covers 3 of one color).