Singular Values & the SVD · Superchallenge problem

Let $A = \begin{pmatrix}1 & 1\\0 & 1\end{pmatrix}$ and let $K = A\otimes A$ be the $4\times 4$ Kronecker product. Find the condition number $\kappa(K) = \sigma_{\max}(K)/\sigma_{\min}(K)$. Give an exact answer.