Engineering stress$-$strain data are plotted above for a portion of a tension test on $7075$T$651$ Aluminum. Note that data points A and $B$ are labeled with their stress strain coordinates. The test bar has dimensions of $150$ mm in length and $12$ mm in diameter. Find the following parameters:

a$)$ Approximate value of the elastic modulus E$?$

b$)$ Yield strength $($determined by a plastic strain offset of $\mathrm{.}002(0\mathrm{.}2\%)?$

c$)$ If the bar is strained to the point $B$ and then unloaded, what is the plastic $($permanent$)$ strain that remains after unloading?

d$)$ If the bar is strained to the point B and then unloaded, what is the length of the bar after unloading?

e$)$ If the bar is strained to the point A$,$ what is the length of the bar at A and after unloading?

f$)$ What is the Elastic Strain Energy Density $(U_r)?$

g$)$ What is the internal Strain Energy Density $(u)$ in the bar and the external work done $(U)$ by the load at $B?$