Given the stress tensor at a point $P$ :

$=\left[\begin{array}{ccc}7& 0& -2\\ 0& 5& 0\\ -2& 0& 4\end{array}\right](MPa)$

$(1)$ Find the traction vector on the plane at $P$ whose unit normal is $n=(\frac{2}{3},-\frac{2}{3},\frac{1}{3}).$

$(2)$ Find the normal stress component perpendicular to the plane.

$(3)$ Find the magnitude of the traction vector.

$(4)$ Find the angle between the traction vector and $n.$