HSN-VM Tutor Intake — Vectors and Matrices

A weather report says "the wind is blowing at 15 miles per hour."
Which statement best explains why this is incomplete as a vector
description of wind?

A vector is labeled $\mathbf{v}$. Which of the following expressions
represents the magnitude of $\mathbf{v}$, not the vector itself?

Matrix $A$ has 3 rows and 4 columns. Matrix $B$ has 4 rows and
2 columns. Which statement about the product $AB$ is correct?

A vector has initial point $(1, 5)$ and terminal point $(4, 2)$.
Enter the component form of this vector as an ordered pair $(a, b)$,
where $a$ is the horizontal component and $b$ is the vertical component.
(Example format: $(3, -4)$)

A vector has components $\langle -5, 12 \rangle$. What is the magnitude
of this vector? Enter an exact value (integer or simplified radical).

Vectors $\mathbf{u} = \langle 3, -1 \rangle$ and $\mathbf{w} = \langle -2, 5 \rangle$.
Compute $\mathbf{u} + \mathbf{w}$ and enter the result as an ordered pair $(a, b)$.
(Example format: $(1, 4)$)

Vectors $\mathbf{v} = \langle 6, 2 \rangle$ and $\mathbf{w} = \langle 4, 7 \rangle$.
Compute $\mathbf{v} - \mathbf{w}$ and enter the result as an ordered pair $(a, b)$.
(Example format: $(2, -5)$)

Vector $\mathbf{v} = \langle 4, -3 \rangle$. Compute $-2\mathbf{v}$ and
enter the result as an ordered pair $(a, b)$.
(Example format: $(-8, 6)$)

Matrix $A = \begin{bmatrix} 5 & 1 & 8 \\ 3 & 7 & 2 \end{bmatrix}$.
What is the value of entry $a_{23}$?
(Enter a single number.)

Matrices $A = \begin{bmatrix} 2 & 1 \\ 0 & 3 \end{bmatrix}$ and
$B = \begin{bmatrix} 4 & -1 \\ 2 & 5 \end{bmatrix}$.
What is the $(1, 2)$ entry of the matrix product $AB$?
That is, what is the value in row 1, column 2 of $AB$?
(Enter a single number.)