Homework #3
The coordinate system in the figure below has been transformed so that
all three axes form equal angles with the original \(z\)axis, and the new
\(x'\)axis is directly above the original \(x\)axis.
Note  this orientation corresponds to the orientation of many
atomic crystals in face centered cubic (FCC) metals undergoing
tension in the Zdirection. Common FCC metals are aluminum, copper,
nickel, and steels at very high temperatures. Steel at room temperature
is body centered cubic (BCC).

What set of Roe angles will produce this transformation?

What single rotation axis and angle will produce the transformation?

A 2D problem:
Given \( \quad {\bf v} = (5,9) \) and
\(\quad {\bf A} = \left[
\matrix {
5 & 2 \\
2 & 3
} \right] \quad
\),
apply a 180° coordinate rotation to both and show that the signs
of all the components change on one but not the other. Any insight
on this?

Show that
\(
\nabla \cdot \nabla  {\bf x}  = 2 /  {\bf x} 
\)