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

$A$ square,of each side $2$,lies above the $x-$axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle $30^o$ with the positive direction of the $x-$axis,then the sum of the $x-$coordinates of the vertices of the square is

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) $f_3(x, y) \longrightarrow \left(\frac{x-y}{2}, \frac{x+y}{2}\right)$

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

The point of intersection of the diagonals of a square is at the origin,and the coordinate axes are drawn along the diagonals. If the side length of the square is $a$,then which of the following is $NOT$ a vertex of the square?

The points $(-a, -b)$,$(0, 0)$,$(a, b)$,and $(a^2, ab)$ are