Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
T: R² R² rotates points (about the origin) through 31/2 radians (in the counterclockwise direction).

T: R² R² rotates points (about the origin) through 31/2 radians (in the counterclockwise direction).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

Assume that T is a linear transformation. Find the standard matrix of T. 

### Rotation Transformation in the Plane Let \( T : \mathbb{R}^2 \rightarrow \mathbb{R}^2 \) be a transformation that rotates points around the origin. The transformation \( T \) rotates points by an angle of \( \frac{3\pi}{2} \) radians in the counterclockwise direction. In mathematical terms, given a point \((x, y)\) in the plane, the transformation \( T \) maps this point to a new point \((x', y')\) after rotating it \( \frac{3\pi}{2} \) radians counterclockwise around the origin. This type of transformation is essential in various fields including geometry, physics, and computer graphics, where understanding how points move under rotation is crucial. For a visual explanation, imagine the \( x \)-\( y \) coordinate plane with the point \((1, 0)\). After applying the rotation transformation \( T \), the point will move along the circle centered at the origin by \( \frac{3\pi}{2} \) radians counterclockwise, resulting in the new position of \((0, -1)\).
Transcribed Image Text:### Rotation Transformation in the Plane Let \( T : \mathbb{R}^2 \rightarrow \mathbb{R}^2 \) be a transformation that rotates points around the origin. The transformation \( T \) rotates points by an angle of \( \frac{3\pi}{2} \) radians in the counterclockwise direction. In mathematical terms, given a point \((x, y)\) in the plane, the transformation \( T \) maps this point to a new point \((x', y')\) after rotating it \( \frac{3\pi}{2} \) radians counterclockwise around the origin. This type of transformation is essential in various fields including geometry, physics, and computer graphics, where understanding how points move under rotation is crucial. For a visual explanation, imagine the \( x \)-\( y \) coordinate plane with the point \((1, 0)\). After applying the rotation transformation \( T \), the point will move along the circle centered at the origin by \( \frac{3\pi}{2} \) radians counterclockwise, resulting in the new position of \((0, -1)\).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS