Task $6$:

A $45$ strain rosette was placed on an implanted plate and the following strains were measured: ${}_a=650({10}^{-6}),{}_b=-230({10}^{-6}),{}_c=-480({10}^{-6}).$ Determine $($a$)$ the principal strain ${}_1$ and the angle of transformation and $($b$)$ the maximum inplane shear strain.

Express your answer to three significant figures and include the appropriate units.

Principal strain ${}_1$

$-{662}^{**{10}^{-6}}(1360({10}^{-6})){}_{p1}$:dots$-11\mathrm{.}1-$dots$(-41\mathrm{.}9$ degrees$)$ Yin plane max:

${1\mathrm{.}15}^{**}{10}^{-3}(1600({10}^{-6})$ radians $)$