The square region $a-b-c-d$ in the reference configuration $K_0$ endures a homogenous deformation to a rectangular region $a^{\text{'}}-b^{\text{'}}-c^{\text{'}}-d^{\text{'}}$ in the deformed configuration $K_t$ as shown below. $($Assume $2$D$)$

$[20$ Poi

a$.$ Find the deformation gradient $[F{]}_e.$

b$.$ Find $[R{]}_e$ and $[U{]}_e,$ where $F=RU.$

c$.$ Find $[Q{]}_e$ and $[V{]}_e,$ where $F=VQ.$

d$.$ Principal direction and values of the stretch

$($HINT: V will be in diagonal form already. Find the corresponding Eigenvector.$)$