Chapter 7 - Eigenvalues and Eigenvectors - Review Exercises - Page 386: 35

orthogonally diagonalizable

A matrix is symmetric if it is equal to its transpose. Also, a matrix is orthogonally diagonalizable if and only if it is symmetric. Here the transpose of the matrix is $\begin{bmatrix} -3& -2 \\ -1& -2\\ \end{bmatrix} $, which is the same as the original matrix, thus it is symmetric; thus it is orthogonally diagonalizable.