Solution
= Solution
Direct multiplication and the identities $\cos^2\theta+\sin^2\theta=1$ and $\cosh^2\theta-\sinh^2\theta=1$ give
$$
\boxed{RR^T=I},
\qquad
\boxed{SJS=J},
\qquad
J=\begin{pmatrix}1&0\\0&-1\end{pmatrix}.
$$
\b[Thus $R$ is an <orthogonal matrix>, while $S$ preserves the indefinite <quadratic form> $x_1^2-x_2^2$.]