Vector $\vec{A}$ has magnitude $3.0 \mathrm{~m}$ and points to the right; vector $\vec{B}$ has magnitude $4.0 \mathrm{~m}$ and points vertically upward. Find the magnitude and direction of vector $\vec{C}$ such that $\vec{A}+\vec{B}+\vec{C}=\overrightarrow{0}$.

Take a point $\mathrm{A}$ in the coordinate plane. Draw the position vector $\mathrm{OA}$ and find the exact value of its magnitude (length). Vary the point $A$ and find the magnitude of $\overrightarrow{\mathrm{O} A}$.

what is the formula you used to find the magnitude?

You need to make a spring scale for measuring mass. You want each $1.0 \mathrm{~cm}$ length along the scale to correspond to a mass difference of $100 \mathrm{~g}$. What should be the value of the spring constant?

You dilate a figure using a scale factor of 2, and then translate it 3 units right. Your friend translates the same figure 3 units right and then dilates it using a scale factor of 2. Are the images congruent? Explain.

What is the magnitude of $\vec{F_2}$ ?

Two long, stralght wires are parallel to each other. The wires carry currents of different magnttudes. If the amount of current flowing in each wire ss doubled, the magnitude of the force between the wires will be a) twlce the magnttude of the orlginal force. b) four times the magnitude of the orlghal force. c) the same as the magnitude of the ortginal force. d) half of the magnitude of the original force.

The scale factor is equal to the ratio $\frac{\text{new length}}{\text{old length}}$ between any two consecutive stages. The scale factor between Stage $1$ and Stage $2$ is $\underline{\quad\quad\quad}$.

Scores on a dental anxiety scale range from 0 (no anxiety) to 20 (extreme anxiety). The scores are normally distributed with a mean of 11 and a standard deviation of 4. Find the z-score for the given score on this dental anxiety scale. 12

Scores on a dental anxiety scale range from 0 (no anxiety) to 20 (extreme anxiety). The scores are normally distributed with a mean of 11 and a standard deviation of 4. Find the z-score for the given score on this dental anxiety scale. 5

You have just joined an exclusive health club, located on the top floor of a skyscraper. You reach the facility by using an express elevator. The elevator has a precision scale installed so that members can weigh themselves before and after their workouts. A member steps into the elevator and gets on the scale before the elevator doors close. The scale shows a weight of $183.7 \mathrm{lb}$. Then the elevator accelerates upward with an acceleration of $2.43 \mathrm{~m} / \mathrm{s}^2$, while the member is still standing on the scale. What is the weight shown by the scale's display while the elevator is accelerating?

Which one of the given situations would a Wilcoxon rank-sum (or Mann-Whitney) test be suitable?

a) Comparing the ratings of a new product on a 5-point Likert scale by a panel of consumers to their ratings of a competitor's product on the same scale.

What is the magnitude of their centripetal acceleration?

Scores on a dental anxiety scale range from 0 (no anxiety) to 20 (extreme anxiety). The scores are normally distributed with a mean of 11 and a standard deviation of 4. Find the z-score for the given score on this dental anxiety scale. 20

A point particle of mass $m$ is moving with a constant speed $v$ along a straight line that passes through point $P$. What can you say about the angular momentum of the particle relative to point $P$ ?

$(a)$ Its magnitude is $m v$.

$(b)$ Its magnitude is zero.

$(c)$ Its magnitude changes sign as the particle passes through point $P$.

$(d)$ Its magnitude increases as the particle approaches point $P$.