A rotation is one of three rigid motions that move a figure in a plane without changing its size or shape. As its name implies, a rotation moves a figure by rotating it around a center somewhere on a plane. This center can be somewhere inside or on the figure, or outside the figure completely. The two other rigid motions are reflections and translations.

Figure 1 illustrates a rotation of 30° around a point C.

This rotation is counterclockwise, which is considered positive. Clockwise rotations are negative. The "product" of two rotations, that is, following one rotation with another, is also a rotation. This assumes that the center of rotation is the same for both. When one moves a heavy box across the room by rotating it first on one corner then on the other, that "product" is not a rotation.

Rotations are so commonplace that it is easy...