Solution
= Solution
A positive, counterclockwise <rotation> takes the standard <basis> vectors $(1,0)^T$ and $(0,1)^T$ to $(\cos\theta,\sin\theta)^T$ and $(-\sin\theta,\cos\theta)^T$. These images are the columns of its <rotation matrix>, so
$$
\boxed{R(\theta)=\begin{pmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{pmatrix}.}
$$
It fixes the origin, preserves the <dot product> and has <determinant> one.