(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.)

A point \( B(-4,4) \) is rotated \( 90^{\circ} \) clockwise about the origin. FInc (A) \( (4,4) \) (B) \( (3,2) \) (C) \( (-3,2) \) (D) \( (4,-4) \)

17. ROSEs The Garden club has a garden in the shape of a right triangle, If one leg is 16 feet long and the hypotenuse is 20 feet long, how long is the remaining leg, along which the roses are planted? Round to the nearest tenth if necessary.

Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: \( (-3,0),(3,0) \); vertices: \( (-10,0),(10,0) \) Type the standard form of the equation. (Type an equation. Simplify your answer.)

Which of the following describes supplementary angles? A. Angles that areadjacent. B. Two or more angles whose sum equals 360 degrees. C. Two angles whose sumequals 180 degrees. D. Angles whose measurements equal 90 degrees.

Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: \( (-2,0),(2,0) ; y \)-intercepts: -9 and 9 Type the standard form of the equation. (Type an equation. Simplify your answer.)