#rotation

For $f(\mathbf{x}) = 0.1x_1^2 + 2x_2^2$ the Hessian is $\textrm{diag}(0.2, 4)$, and diagonal preconditioning brings the condition number from 20 down to 1. Rotating the problem by $45^\circ$ (and doubling it, which does not change any condition number) gives $f(\mathbf{x}) = 0.1(x_1 + x_2)^2 + 2(x_1 - x_2)^2$. What is the condition number of $D^{-1/2}\mathbf{H}D^{-1/2}$, with $D = \textrm{diag}(\mathbf{H})$, for the rotated function?