#### Answer

(a) $A \cdot B = -2$
(b) $A \cdot B = 0$

#### Work Step by Step

We can use the formula for the dot product of two vectors $A$ and $B$:
$A\cdot B = A_x~B_x + A_y~B_y$
(a) $A \cdot B = A_x~B_x + A_y~B_y$
$A \cdot B = (4)(-2)+(-2)(-3)$
$A \cdot B = -2$
(b) $A \cdot B = A_x~B_x + A_y~B_y$
$A \cdot B = (-4)(2)+(2)(4)$
$A \cdot B = 0$