Refer a friend and earn $50 when they subscribe to an annual planRefer Now
Get the answer to your homework problem.
Try Numerade Free for 30 Days
Like
Report
Show that the transformation in Exercise 8 is merely a rotation about the origin. What is the angle of the rotation?
The angle of rotation is $\frac{\pi}{2}$ or 90 deg.
Algebra
Chapter 1
Linear Equations in Linear Algebra
Section 9
The Matrix of a Linear Transformation
Introduction to Matrices
McMaster University
Harvey Mudd College
Baylor University
University of Michigan - Ann Arbor
Lectures
01:32
In mathematics, the absolu…
01:11
00:36
Find the degree measure of…
00:41
00:32
04:13
Show that the transformati…
00:35
00:43
00:38
Find the radian measure of…
00:42
04:40
Find a new representation …
00:31
Determine the coordinates …
So we want to use the transformation from exercise east. And so we have this, uh, matrix t just the standard metrics. So we know that the first call in is t of anyone, and the second call is t of each ago. Maybe we should call this something different. Well, call it a so we wouldn't show that this is just a rotation about the origin. And we want to find out how many degrees directors are being rotated. So we know the one iss vector 10 And he, too, was the vector zero. So let's go ahead and plot the map ings. So we want is 10 So that is this rector here, and we know that after reply the transformation t t of the one is 01 because that's the first column. So is he wrote one hiss inspector here so we can see that our original vector the one is rotated, uh, counterclockwise, 90 degrees. So let's do the same thing with me too. So you two whoops is the factor. 10 We're sorry. 01 Which is the specter here? And TV, too? It's the second column, which is negative 10 which is this factor here. So I can see again. As in the first case, our director is rotated to the left about the origin 90 degrees. So we have a, uh our degree of rotation ISS to the left. So it's negative. We can say negative 90 degrees or negative pi over to radiance.
View More Answers From This Book
Find Another Textbook
In mathematics, the absolute value or modulus |x| of a real number x is its …
Find the degree measure of the angles. Keeping in mind that an angle of one …
Show that the transformation in Exercise 7 is equivalent to a rotation about…
Find the radian measure of each angle. keeping in mind that an angle of one …
Find a new representation of the given equation after rotating through the g…
Determine the coordinates of each point after a rotation about the origin by…
01:16
Do the three lines $x_{1}-4 x_{2}=1,2 x_{1}-x_{2}=-3,$ and $-x_{1}-3 x_{2}=4…
02:05
Let $T : \mathbb{R}^{n} \rightarrow \mathbb{R}^{m}$ be a linear transformati…
[M] In Exercises $37-40$ , determine if the columns of the matrix span $\mat…
$[\mathbf{M}]$ In Exercises $37-40,$ let $T$ be the linear transformation wh…
02:19
Give a geometric description of $\operatorname{Span}\left\{\mathbf{v}_{1}, \…
03:09
Suppose $A$ is an $m \times n$ matrix and there exist $n \times m$ matrices …
12:10
In Exercises 3 and $4,$ display the following vectors using arrows on an $x …
01:55
Why is the question "Is the linear transformation $T$ onto?" an ex…
04:16
[M] Study how changes in boundary temperatures on a steel plate affect the t…
10:34
Show that if the columns of $B$ are linearly dependent, then so are the colu…
92% of Numerade students report better grades.
Try Numerade Free for 30 Days. You can cancel at any time.
Annual
0.00/mo 0.00/mo
Billed annually at 0.00/yr after free trial
Monthly
0.00/mo
Billed monthly at 0.00/mo after free trial
Earn better grades with our study tools:
Textbooks
Video lessons matched directly to the problems in your textbooks.
Ask a Question
Can't find a question? Ask our 30,000+ educators for help.
Courses
Watch full-length courses, covering key principles and concepts.
AI Tutor
Receive weekly guidance from the world’s first A.I. Tutor, Ace.
30 day free trial, then pay 0.00/month
30 day free trial, then pay 0.00/year
You can cancel anytime
OR PAY WITH
Your subscription has started!
The number 2 is also the smallest & first prime number (since every other even number is divisible by two).
If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".
Receive weekly guidance from the world's first A.I. Tutor, Ace.
Mount Everest weighs an estimated 357 trillion pounds
Snapshot a problem with the Numerade app, and we'll give you the video solution.
A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.
Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.