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The vector $\langle 2, 1 \rangle$ starts at the point $(1, 1)$ . Tap the point where it ends.
$P = (3, 3)$ and $Q = (8, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 5 \rangle$
2. $\langle -5, -5 \rangle$
3. $\langle 11, 11 \rangle$
$P = (2, 2)$ and $Q = (8, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 4 \rangle$
2. $\langle -6, -4 \rangle$
3. $\langle 10, 8 \rangle$
$P = (2, 2)$ and $Q = (8, 5)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 3 \rangle$
2. $\langle -6, -3 \rangle$
3. $\langle 10, 7 \rangle$
$P = (1, 4)$ and $Q = (7, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 3 \rangle$
2. $\langle -6, -3 \rangle$
3. $\langle 8, 11 \rangle$
$P = (3, 4)$ and $Q = (6, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 4 \rangle$
2. $\langle -3, -4 \rangle$
3. $\langle 9, 12 \rangle$
$P = (4, 1)$ and $Q = (5, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 1, 5 \rangle$
2. $\langle -1, -5 \rangle$
3. $\langle 9, 7 \rangle$
$P = (4, 2)$ and $Q = (7, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 4 \rangle$
2. $\langle -3, -4 \rangle$
3. $\langle 11, 8 \rangle$
$P = (4, 1)$ and $Q = (5, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 1, 6 \rangle$
2. $\langle -1, -6 \rangle$
3. $\langle 9, 8 \rangle$
$P = (3, 3)$ and $Q = (6, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 4 \rangle$
2. $\langle -3, -4 \rangle$
3. $\langle 9, 10 \rangle$
$P = (2, 3)$ and $Q = (6, 9)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 4, 6 \rangle$
2. $\langle -4, -6 \rangle$
3. $\langle 8, 12 \rangle$
$P = (1, 1)$ and $Q = (6, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 5 \rangle$
2. $\langle -5, -5 \rangle$
3. $\langle 7, 7 \rangle$
$P = (2, 3)$ and $Q = (5, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 5 \rangle$
2. $\langle -3, -5 \rangle$
3. $\langle 7, 11 \rangle$
$P = (1, 2)$ and $Q = (8, 9)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 7, 7 \rangle$
2. $\langle -7, -7 \rangle$
3. $\langle 9, 11 \rangle$
$P = (3, 3)$ and $Q = (6, 5)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 2 \rangle$
2. $\langle -3, -2 \rangle$
3. $\langle 9, 8 \rangle$
$P = (2, 4)$ and $Q = (9, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 7, 2 \rangle$
2. $\langle -7, -2 \rangle$
3. $\langle 11, 10 \rangle$
$P = (4, 1)$ and $Q = (7, 5)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 4 \rangle$
2. $\langle -3, -4 \rangle$
3. $\langle 11, 6 \rangle$
$P = (2, 2)$ and $Q = (6, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 4, 6 \rangle$
2. $\langle -4, -6 \rangle$
3. $\langle 8, 10 \rangle$
$P = (2, 3)$ and $Q = (9, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 7, 5 \rangle$
2. $\langle -7, -5 \rangle$
3. $\langle 11, 11 \rangle$
$P = (3, 4)$ and $Q = (6, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 3 \rangle$
2. $\langle -3, -3 \rangle$
3. $\langle 9, 11 \rangle$
$P = (1, 1)$ and $Q = (9, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 8, 5 \rangle$
2. $\langle -8, -5 \rangle$
3. $\langle 10, 7 \rangle$
$P = (4, 3)$ and $Q = (7, 9)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 6 \rangle$
2. $\langle -3, -6 \rangle$
3. $\langle 11, 12 \rangle$
$P = (3, 3)$ and $Q = (9, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 4 \rangle$
2. $\langle -6, -4 \rangle$
3. $\langle 12, 10 \rangle$
$P = (3, 1)$ and $Q = (9, 9)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 8 \rangle$
2. $\langle -6, -8 \rangle$
3. $\langle 12, 10 \rangle$
$P = (4, 1)$ and $Q = (9, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 5 \rangle$
2. $\langle -5, -5 \rangle$
3. $\langle 13, 7 \rangle$
$P = (2, 3)$ and $Q = (6, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 4, 5 \rangle$
2. $\langle -4, -5 \rangle$
3. $\langle 8, 11 \rangle$
$P = (3, 1)$ and $Q = (8, 9)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 8 \rangle$
2. $\langle -5, -8 \rangle$
3. $\langle 11, 10 \rangle$
$P = (1, 2)$ and $Q = (9, 5)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 8, 3 \rangle$
2. $\langle -8, -3 \rangle$
3. $\langle 10, 7 \rangle$
$P = (4, 3)$ and $Q = (9, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 4 \rangle$
2. $\langle -5, -4 \rangle$
3. $\langle 13, 10 \rangle$
$P = (3, 3)$ and $Q = (9, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 5 \rangle$
2. $\langle -6, -5 \rangle$
3. $\langle 12, 11 \rangle$
$P = (2, 2)$ and $Q = (9, 9)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 7, 7 \rangle$
2. $\langle -7, -7 \rangle$
3. $\langle 11, 11 \rangle$
$P = (2, 1)$ and $Q = (7, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 5 \rangle$
2. $\langle -5, -5 \rangle$
3. $\langle 9, 7 \rangle$
$P = (1, 2)$ and $Q = (8, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 7, 6 \rangle$
2. $\langle -7, -6 \rangle$
3. $\langle 9, 10 \rangle$
$P = (3, 1)$ and $Q = (7, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 4, 7 \rangle$
2. $\langle -4, -7 \rangle$
3. $\langle 10, 9 \rangle$
$P = (1, 3)$ and $Q = (7, 9)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 6 \rangle$
2. $\langle -6, -6 \rangle$
3. $\langle 8, 12 \rangle$
$P = (2, 2)$ and $Q = (5, 5)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 3 \rangle$
2. $\langle -3, -3 \rangle$
3. $\langle 7, 7 \rangle$
$P = (3, 3)$ and $Q = (6, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 3 \rangle$
2. $\langle -3, -3 \rangle$
3. $\langle 9, 9 \rangle$
$P = (2, 1)$ and $Q = (7, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 6 \rangle$
2. $\langle -5, -6 \rangle$
3. $\langle 9, 8 \rangle$
$P = (1, 1)$ and $Q = (6, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 6 \rangle$
2. $\langle -5, -6 \rangle$
3. $\langle 7, 8 \rangle$
$P = (2, 3)$ and $Q = (8, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 4 \rangle$
2. $\langle -6, -4 \rangle$
3. $\langle 10, 10 \rangle$
$P = (4, 3)$ and $Q = (5, 5)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 1, 2 \rangle$
2. $\langle -1, -2 \rangle$
3. $\langle 9, 8 \rangle$
$P = (2, 3)$ and $Q = (9, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 7, 4 \rangle$
2. $\langle -7, -4 \rangle$
3. $\langle 11, 10 \rangle$
$P = (1, 1)$ and $Q = (8, 5)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 7, 4 \rangle$
2. $\langle -7, -4 \rangle$
3. $\langle 9, 6 \rangle$
$P = (1, 4)$ and $Q = (6, 9)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 5 \rangle$
2. $\langle -5, -5 \rangle$
3. $\langle 7, 13 \rangle$
$P = (3, 1)$ and $Q = (8, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 5 \rangle$
2. $\langle -5, -5 \rangle$
3. $\langle 11, 7 \rangle$
$P = (3, 4)$ and $Q = (7, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 4, 2 \rangle$
2. $\langle -4, -2 \rangle$
3. $\langle 10, 10 \rangle$
$P = (3, 2)$ and $Q = (5, 5)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 2, 3 \rangle$
2. $\langle -2, -3 \rangle$
3. $\langle 8, 7 \rangle$
$P = (2, 4)$ and $Q = (7, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 4 \rangle$
2. $\langle -5, -4 \rangle$
3. $\langle 9, 12 \rangle$
$P = (2, 2)$ and $Q = (5, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 5 \rangle$
2. $\langle -3, -5 \rangle$
3. $\langle 7, 9 \rangle$
$P = (2, 1)$ and $Q = (9, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 7, 6 \rangle$
2. $\langle -7, -6 \rangle$
3. $\langle 11, 8 \rangle$
$P = (3, 2)$ and $Q = (9, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 4 \rangle$
2. $\langle -6, -4 \rangle$
3. $\langle 12, 8 \rangle$
A plane flies due east at 101 miles per hour through the air, and the wind blows due north at 32 miles per hour. Find its speed over the ground, to 1 decimal place.Not to scale
Two people pull a box: one with 36 newtons due east, the other with 59 newtons due north. At what angle north of east does the box start to move? Give degrees to 1 decimal place.Not to scale
Let A = $\begin{pmatrix} 3 & -3 \\ 7 & 5 \end{pmatrix}$ and B = $\begin{pmatrix} -4 & -4 \\ -5 & 5 \end{pmatrix}$ . What is the entry in row 1, column 2 of A + B?
Let A = $\begin{pmatrix} 2 & 0 \\ 6 & 2 \end{pmatrix}$ . What is the entry in row 2, column 1 of 3A?
A shop records sales in a matrix with one row for each of its 4 stores and one column for each of 7 days. What are the dimensions of the matrix?
1. 4 × 7
2. 7 × 4
3. 28 × 1
A shop records sales in a matrix with one row for each of its 2 stores and one column for each of 6 days. What are the dimensions of the matrix?
1. 2 × 6
2. 6 × 2
3. 12 × 1
A shop records sales in a matrix with one row for each of its 4 stores and one column for each of 6 days. What are the dimensions of the matrix?
1. 4 × 6
2. 6 × 4
3. 24 × 1
A shop records sales in a matrix with one row for each of its 3 stores and one column for each of 7 days. What are the dimensions of the matrix?
1. 3 × 7
2. 7 × 3
3. 21 × 1
A shop records sales in a matrix with one row for each of its 2 stores and one column for each of 7 days. What are the dimensions of the matrix?
1. 2 × 7
2. 7 × 2
3. 14 × 1
A shop records sales in a matrix with one row for each of its 3 stores and one column for each of 6 days. What are the dimensions of the matrix?
1. 3 × 6
2. 6 × 3
3. 18 × 1
A shop records sales in a matrix with one row for each of its 2 stores and one column for each of 8 days. What are the dimensions of the matrix?
1. 2 × 8
2. 8 × 2
3. 16 × 1
A shop records sales in a matrix with one row for each of its 5 stores and one column for each of 7 days. What are the dimensions of the matrix?
1. 5 × 7
2. 7 × 5
3. 35 × 1
A shop records sales in a matrix with one row for each of its 2 stores and one column for each of 9 days. What are the dimensions of the matrix?
1. 2 × 9
2. 9 × 2
3. 18 × 1
A shop records sales in a matrix with one row for each of its 4 stores and one column for each of 8 days. What are the dimensions of the matrix?
1. 4 × 8
2. 8 × 4
3. 32 × 1
A shop records sales in a matrix with one row for each of its 5 stores and one column for each of 8 days. What are the dimensions of the matrix?
1. 5 × 8
2. 8 × 5
3. 40 × 1
A shop records sales in a matrix with one row for each of its 3 stores and one column for each of 8 days. What are the dimensions of the matrix?
1. 3 × 8
2. 8 × 3
3. 24 × 1
A shop records sales in a matrix with one row for each of its 5 stores and one column for each of 9 days. What are the dimensions of the matrix?
1. 5 × 9
2. 9 × 5
3. 45 × 1
A shop records sales in a matrix with one row for each of its 4 stores and one column for each of 9 days. What are the dimensions of the matrix?
1. 4 × 9
2. 9 × 4
3. 36 × 1
A shop records sales in a matrix with one row for each of its 3 stores and one column for each of 9 days. What are the dimensions of the matrix?
1. 3 × 9
2. 9 × 3
3. 27 × 1
A shop records sales in a matrix with one row for each of its 5 stores and one column for each of 6 days. What are the dimensions of the matrix?
1. 5 × 6
2. 6 × 5
3. 30 × 1
Let A = $\begin{pmatrix} 4 & 2 \\ 3 & -2 \end{pmatrix}$ and B = $\begin{pmatrix} 7 & 9 \\ 5 & 4 \end{pmatrix}$ . What is the entry in row 1, column 1 of AB?
Let A = $\begin{pmatrix} 8 & 8 \\ 8 & 4 \end{pmatrix}$ and B = $\begin{pmatrix} 2 & 3 \\ 3 & 2 \end{pmatrix}$ . What is the entry in row 2, column 1 of AB?
A is a 2 × 5 matrix and B is a 5 × 8 matrix. What are the dimensions of AB?
1. 2 × 8
2. 5 × 5
3. AB is not defined
A is a 4 × 5 matrix and B is a 5 × 8 matrix. What are the dimensions of AB?
1. 4 × 8
2. 5 × 5
3. AB is not defined
A is a 4 × 6 matrix and B is a 6 × 7 matrix. What are the dimensions of AB?
1. 4 × 7
2. 6 × 6
3. AB is not defined
A is a 3 × 5 matrix and B is a 5 × 9 matrix. What are the dimensions of AB?
1. 3 × 9
2. 5 × 5
3. AB is not defined
A is a 2 × 6 matrix and B is a 6 × 9 matrix. What are the dimensions of AB?
1. 2 × 9
2. 6 × 6
3. AB is not defined
A is a 3 × 6 matrix and B is a 6 × 8 matrix. What are the dimensions of AB?
1. 3 × 8
2. 6 × 6
3. AB is not defined
A is a 3 × 5 matrix and B is a 5 × 8 matrix. What are the dimensions of AB?
1. 3 × 8
2. 5 × 5
3. AB is not defined
A is a 3 × 5 matrix and B is a 5 × 7 matrix. What are the dimensions of AB?
1. 3 × 7
2. 5 × 5
3. AB is not defined
A is a 3 × 6 matrix and B is a 6 × 7 matrix. What are the dimensions of AB?
1. 3 × 7
2. 6 × 6
3. AB is not defined
A is a 2 × 6 matrix and B is a 6 × 8 matrix. What are the dimensions of AB?
1. 2 × 8
2. 6 × 6
3. AB is not defined
A is a 4 × 5 matrix and B is a 5 × 7 matrix. What are the dimensions of AB?
1. 4 × 7
2. 5 × 5
3. AB is not defined
A is a 4 × 6 matrix and B is a 6 × 8 matrix. What are the dimensions of AB?
1. 4 × 8
2. 6 × 6
3. AB is not defined
A is a 2 × 6 matrix and B is a 6 × 7 matrix. What are the dimensions of AB?
1. 2 × 7
2. 6 × 6
3. AB is not defined
A is a 2 × 5 matrix and B is a 5 × 7 matrix. What are the dimensions of AB?
1. 2 × 7
2. 5 × 5
3. AB is not defined
A is a 4 × 5 matrix and B is a 5 × 9 matrix. What are the dimensions of AB?
1. 4 × 9
2. 5 × 5
3. AB is not defined
A is a 4 × 6 matrix and B is a 6 × 9 matrix. What are the dimensions of AB?
1. 4 × 9
2. 6 × 6
3. AB is not defined
A is a 3 × 6 matrix and B is a 6 × 9 matrix. What are the dimensions of AB?
1. 3 × 9
2. 6 × 6
3. AB is not defined
A is a 2 × 5 matrix and B is a 5 × 9 matrix. What are the dimensions of AB?
1. 2 × 9
2. 5 × 5
3. AB is not defined
Let A = $\begin{pmatrix} 9 & 2 \\ 3 & 6 \end{pmatrix}$ . What is the first component of A $\begin{pmatrix} -3 \\ -1 \end{pmatrix}$ ?
The matrix $\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ maps the point (8, 0) to (0, 8) and (0, 8) to (−8, 0). Which transformation does it represent?
1. A rotation of 90° counterclockwise about the origin
2. A reflection in the line y = x
3. A rotation of 90° clockwise about the origin
The matrix $\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ maps the point (4, 0) to (0, 4) and (0, 4) to (−4, 0). Which transformation does it represent?
1. A rotation of 90° counterclockwise about the origin
2. A reflection in the line y = x
3. A rotation of 90° clockwise about the origin
The matrix $\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ maps the point (7, 0) to (0, 7) and (0, 7) to (−7, 0). Which transformation does it represent?
1. A rotation of 90° counterclockwise about the origin
2. A reflection in the line y = x
3. A rotation of 90° clockwise about the origin
The matrix $\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ maps the point (6, 0) to (0, 6) and (0, 6) to (−6, 0). Which transformation does it represent?
1. A rotation of 90° counterclockwise about the origin
2. A reflection in the line y = x
3. A rotation of 90° clockwise about the origin
The matrix $\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ maps the point (3, 0) to (0, 3) and (0, 3) to (−3, 0). Which transformation does it represent?
1. A rotation of 90° counterclockwise about the origin
2. A reflection in the line y = x
3. A rotation of 90° clockwise about the origin
The matrix $\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ maps the point (1, 0) to (0, 1) and (0, 1) to (−1, 0). Which transformation does it represent?
1. A rotation of 90° counterclockwise about the origin
2. A reflection in the line y = x
3. A rotation of 90° clockwise about the origin
The matrix $\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ maps the point (9, 0) to (0, 9) and (0, 9) to (−9, 0). Which transformation does it represent?
1. A rotation of 90° counterclockwise about the origin
2. A reflection in the line y = x
3. A rotation of 90° clockwise about the origin
The matrix $\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ maps the point (5, 0) to (0, 5) and (0, 5) to (−5, 0). Which transformation does it represent?
1. A rotation of 90° counterclockwise about the origin
2. A reflection in the line y = x
3. A rotation of 90° clockwise about the origin
The matrix $\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ maps the point (2, 0) to (0, 2) and (0, 2) to (−2, 0). Which transformation does it represent?
1. A rotation of 90° counterclockwise about the origin
2. A reflection in the line y = x
3. A rotation of 90° clockwise about the origin
A shape with an area of 2 square units is transformed by the matrix $\begin{pmatrix} 2 & 2 \\ 2 & 3 \end{pmatrix}$ . What is the area of the image?

Answers

$(3, 2)$
$\langle 5, 5 \rangle$
$5 \sqrt{449}$
$\frac{180 \tan^{-1}{\left(\frac{59}{36} \right)}}{\pi}$
$-7$
$18$
4 × 7
$38$
$28$
2 × 8
$-29$
A rotation of 90° counterclockwise about the origin
$4$