A rotation matrix is a mathematical tool used to rotate points in a coordinate system. It is typically represented as a square matrix, where the elements are derived from the angle of rotation. In two dimensions, a rotation matrix can be expressed as: \[ \beginpmatrix \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \endpmatrix \] where \theta is the angle of rotation. In three dimensions, rotation matrices become more complex, involving rotations around the x, y, or z axes. These matrices are essential in various fields, including computer graphics, robotics, and physics, as they help in transforming the orientation of objects in space while preserving their shape and size.