Answer:
There are two possibilities
a) If the integers are positives the product will be positive.
b) If the integers are negatives the product will be negative.
Step-by-step explanation:
We need to use rule of signs to explain the answers
for answer "a"
We have (+)(+)( + ) equals positive
for answer "b"
We have (-)(-) = + then this multiply by the last integer which has negative sign
(+)(-) = -
Use the distance of 1 lap to multiply the number of laps ran
Answer:
Step-by-step explanation:
( - 2 , 3 )
( 3 , - 4 )
m =
= -
y - 3 = -
( x - ( - 2 ) )
y = -
x -
+ 3
y = -
x +
I'm not sure exactly about the squared part but that would be going backwards with a rate of -2 m/s.
<h3>Answer:</h3>
(x, y) ⇒ (-y, x)
<h3>Explanation:</h3>
A point at y=1 on the y-axis will rotate to the point x = -1 on the x-axis when it is rotated 90° CCW about the origin. Hence the value of x for the image point is the opposite of the y-value of the original point.
A point at x=1 on the x-axis will rotate to the point y=1 on the y-axis when it is rotated 90° CCW about the origin. Hence the value of y for the image point is the x-value of the original point.
In summary, ...
... (x, y) ⇒ (-y, x)
_____
<em>Comment on rotation matrices</em>
The rotation matrix for rotatation through the angle θ CCW about the origin is ...
![\left[\begin{array}{cc}\cos{(\theta)}&-\sin{(\theta)}\\\sin{(\theta)}&\cos{(\theta)}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Ccos%7B%28%5Ctheta%29%7D%26-%5Csin%7B%28%5Ctheta%29%7D%5C%5C%5Csin%7B%28%5Ctheta%29%7D%26%5Ccos%7B%28%5Ctheta%29%7D%5Cend%7Barray%7D%5Cright%5D)
When θ = 90°, this matrix becomes ...
![\left[\begin{array}{cc}0&-1\\1&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%26-1%5C%5C1%260%5Cend%7Barray%7D%5Cright%5D)
and multiplication by coordinates (x, y) gives ...
![\left[\begin{array}{cc}0&-1\\1&0\end{array}\right]\times\left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}-y\\x\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%26-1%5C%5C1%260%5Cend%7Barray%7D%5Cright%5D%5Ctimes%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-y%5C%5Cx%5Cend%7Barray%7D%5Cright%5D)