Planar rotation
= Planar rotation
{title2=$R_\theta$}
A planar rotation about the origin is the <linear map> represented by the <rotation matrix> $R_\theta=\left(\begin{smallmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{smallmatrix}\right)$. It preserves <inner products>, lengths, oriented angles and area, with positive angles measured anticlockwise. Its inverse is $R_{-\theta}$ and its <determinant> is one.