Asking help how to solve this with detailed steps: Local feature detection and description

Below we have computed the gradients of an image at each pixel:

$($a$)$ Compute the second moment matrix $M$ for the coloured $33$ window $W.$

Assume that the weighting function $w$ is a constant $w(x,y)=1$

$M=\left[\begin{array}{cc}{\displaystyle \underset{x}{\overset{?}{}}},yw(x,y)I_x^2& {\displaystyle \underset{x}{\overset{?}{}}},yw(x,y)I_x{I}_y\\ {\displaystyle \underset{x}{\overset{?}{}}},yw(x,y)I_x{I}_y& {\displaystyle \underset{x}{\overset{?}{}}},yw(x,y)I_y^2\end{array}\right]$

$($b$)$ Compute the value of the corner response function when $=0\mathrm{.}04$ : $R=$det$(M)-$ trace$(M{)}^2$

$($c$)$ How would you characterise the "cornerness" of window $W$ and why?

Let's assume that we detected SIFT regions from two images $($i$.$e$.$ circular regions with assigned orientations$)$ of the same textured plane.

$($d$)$ What is the minimum number of SIFT region correspondence pairs needed for computing a similarity transformation between the pair of images?

$($e$)$ How do we compute a histogram of gradient orientations when generating a SIFT descriptor?