Give a full correct answer for given question

To find: The equivalent polar equation for the given rectangular-coordinate equation.
Given:
${\displaystyle x^2+y^2+8x=0}$

The Cartesian coordinates of a point are given.
a) $(2,-2)$
b) $(-1,\sqrt{3})$
Find the polar coordinates $(r,\theta )$ of the point, where r is greater than 0 and 0 is less than or equal to $\theta$, which is less than $2\pi$
Find the polar coordinates $(r,\theta )$ of the point, where r is less than 0 and 0 is less than or equal to $\theta$, which is less than $2\pi$

Below are various vectors in cartesian, cylindrical and spherical coordinates. Express the given vectors in two other coordinate systems outside the coordinate system in which they are expressed
$a)\overrightarrow{A}(x,y,z)={\overrightarrow{e}}_x$
$d)\overrightarrow{A}(\rho ,\varphi ,z)={\overrightarrow{e}}_{\rho }$
$g)\overrightarrow{A}(r,\theta ,\varphi )={\overrightarrow{e}}_{\theta }$
$j)\overrightarrow{A}(x,y,z)=\frac{-y{\overrightarrow{e}}_x+x{\overrightarrow{e}}_y}{x^2+y^2}$

The equivalent polar equation for the given rectangular-coordinate equation:
${\displaystyle x^2+y^2+8x=0}$

The equivalent polar coordinates for the given rectangular coordinates:
${\displaystyle \left[\begin{array}{cc}4& 0\end{array}\right]}$

Give a correct answer for given question

(A) Argue why $(1,0,3),(2,3,1),(0,0,1)$ is a coordinate system ( bases ) for $R^3$ ?

(B) Find the coordinates of $(7,6,16)$ relative to the set in part (A)

Show that if u is a vector in R^{2} or R&3, then ${\displaystyle u+(-1)u=0}$
${\displaystyle u+(-1)u=0}$