If you've done any sort of work with graphics, you're no doubt familiar with matrix operations — scaling, translating and rotating. In the matrix model of graphics operations, each operation is parameterized by a specific matrix, and the individual coordinates of the shapes to be manipulated are represented as column vectors. Scaling (resizing) and translating (moving) are easy enough to understand (but I'll go ahead and review them briefly anyway), but I've never seen the rotation matrix adequately explained. Most books about linear algebra try to frame rotation matrices around the context of changes of basis of orthogonal vectors (say that five times fast!) — I'm sure that's a useful explanation to somebody, somewhere, but I prefer a geometrical explanation.