If the polar coordinates of a point are $\left( \sqrt{2}, -\frac{3\pi}{4} \right)$,what are its Cartesian coordinates?

If a square $ABCD$,where $A(0,0), B(2,0), C(2,2)$ and $D(0,2)$ undergoes the following transformations successively,then the final figure would be a:
$(i)$ $f_1(x, y) \longrightarrow (y, x)$
(ii) $f_2(x, y) \longrightarrow (x+3y, y)$
(iii) $f_3(x, y) \longrightarrow \left(\frac{x-y}{2}, \frac{x+y}{2}\right)$

The point to which the origin is to be shifted to eliminate $x$ and $y$ terms of the equation $4x^2+9y^2-8x+36y+4=0$ is

If the Cartesian coordinates of a point are $\left(\frac{-5 \sqrt{3}}{2}, \frac{5}{2}\right)$,then its polar coordinates are

The vertices of a figure are $(-2, 2), (-2, -1), (3, -1),$ and $(3, 2)$. This figure is a:

Let $ABCD$ be a square and $E$ be a point outside $ABCD$ such that $E, A, C$ are collinear in that order. Suppose $EB = ED = \sqrt{130}$ and the areas of $\triangle EAB$ and square $ABCD$ are equal. Then,the area of square $ABCD$ is