Calcula el área y perimetro del rectángulo, si su altura es de 21 cm y su diagonal mide 29 cm Si ABCD es un trapecio isósceles, calcular su área y perimetro.

Given \( \mathbf{v}=-9 \mathbf{i} \) and \( \mathbf{w}=-\mathbf{j} \) (a) find the dot product \( \mathbf{v} \cdot \mathbf{w} \) (b) find the angle between \( \mathbf{v} \) and \( \mathbf{w} \); (c) state whether the vectors are parallel, orthogonal, or neither.

(a) Find the dot product \( \mathbf{v} \cdot \mathbf{w} \); (b) find the angle between \( \mathbf{v} \) and \( \mathbf{w} \); (c) state whether the vectors are parallel, orthogonal, or neither. \( \mathbf{v}=\sqrt{3} \mathbf{i}+3 \mathbf{j}, \quad \mathbf{w}=-\mathbf{i}+\mathbf{j} \) (a) \( \mathbf{v} \cdot \mathbf{w}=3-\sqrt{3} \) (Simplify your answer. Type an exact answer, using radicals as needed.) (b) The angle between \( \mathbf{v} \) and \( \mathbf{w} \) is \( \square^{\circ} \). (Type your answer in degrees.)

Given \( \mathbf{v}=-\mathbf{i}+\mathbf{j} \) and \( \mathbf{w}=\mathbf{i}+\mathbf{j} \) (a) find the dot product \( \mathbf{v} \cdot \mathbf{w} \); (b) find the angle between \( \mathbf{v} \) and \( \mathbf{w} \); (c) state whether the vectors are parallel, orthogonal, or neither. (a) \( \mathbf{v} \cdot \mathbf{w}=\square \)

Use the given vectors to find \( \mathbf{v} \cdot \mathbf{w} \) and \( \mathbf{v} \cdot \mathbf{v} \). \[ \begin{array}{l}\mathbf{v}=-7 \mathbf{i}-3 \mathbf{j}, \mathbf{w}=-9 \mathbf{i}-5 \mathbf{j} \\ \mathbf{v} \cdot \mathbf{w}=78 \text { (Simplify your answer.) } \\ \mathbf{v} \cdot \mathbf{v}=\square \text { (Simplify your answer.) }\end{array} \text { \$ } \]

Determina la pendiente de la línea que pasa por los puntos \( (-1, -1) \) y \( (2, 5) \).