If $U=\left[\begin{array}{cc}4& 1\\ 5& 2\end{array}\right]$ answer the following:

a$.$ If the system is under a $30$ rotation in $2$ D $,$ calculate the small strain tensor $lon$ using $($i$)$ the small rotation assumption and $($ii$)$ assuming no rotation. Are they the same? Why or why not? According to you which method is more accurate? Why? $(10$ points$)$

b$.$ If the system is under a $8$ rotation in $2$D$,$ calculate the small strain tensor $lon$ and the Green Strain tensor $E.$ Are they the same? Why or why not? $(10$ points$)$