The strain gauge rosette shown in Fig. Q$1($b$)$ records strain measurements as follows:

${}_a=0\mathrm{.}000225,{}_b=-0\mathrm{.}000100,$ and ${}_c=-0\mathrm{.}000050$

$($i$)$ Determine the magnitude of the principal strains, the maximum in$-$plane shear strain, and the absolute maximum shear strain.

$($ii$)$ Determine the orientation of the maximum principal strain and the orientation of the maximum shear strain relative to the $x-$axis.

$($iii$)$ Determine the principal stresses and the maximum inplane shear stress given $E=190$GPa and $v=0\mathrm{.}33.$

$($iv$)$ Draw and fully annotate a scaled Mohr's $2$D strain circle representing the measured state of strain.