a$.$ Provided the primed stress tensor $=\left[\begin{array}{ccc}500& -200& 100\\ -200& 300& -50\\ 100& -50& 200\end{array}\right]$ and the transformation tensor

$=\left[\begin{array}{ccc}0\mathrm{.}8& 0\mathrm{.}6& 0\\ -0\mathrm{.}48& 0\mathrm{.}64& 0\mathrm{.}6\\ 0\mathrm{.}36& -0\mathrm{.}48& 0\mathrm{.}8\end{array}\right],$ determine the unprimed stress tensor ${}_{ij}.$

b$.$ Provided the cutting plane $n_j=\{\frac{-1\sqrt[\phantom{2}]{14}}{14}\frac{2\sqrt[\phantom{2}]{14}}{14}\frac{3\sqrt[\phantom{2}]{14}}{14}{\}}^T$ and the Cauchy Stress tensor ${}_{ij}=$

$\left[\begin{array}{ccc}500& -200& 100\\ -200& 300& -50\\ 100& -50& 200\end{array}\right],$ determine the stress vector $T_i.$