5. A rotation on a computer screen is sometimes implemented as the product of two shear-and-scale transformations, which can speed up calculations that determine how a graphic image actually appears in terms of screen pixels. (The screen consists of rows and 1 columns of small dots, called pixels.) The first transformation A, shears vertically and then compresses each column of pixels; the second transformation A₂ shears horizontally and then stretches each row of pixels. Let A₁ = A₂ = seco 0 0 tano 0 10, and show that the composition of the two transformations is a rotation in 01 Which composition of the transformations represents the rotation? OA. A₁ A₂ OB. A₂A₁ Write the 3x3 matrix that corresponds to the composite transformation. Explain why the composition of the two transformations is a rotation in R². The composition of the two transformations is the transformation matrix in homogeneous coordinates for a (1) O clockwise (1) 1 O counterclockwise (2) O angle 0 000 (Simplify your answers.) O angle p O angle √ O angle ² rotation about the origin at (2) in R². 00 sin cos 0 and 0 01
5. A rotation on a computer screen is sometimes implemented as the product of two shear-and-scale transformations, which can speed up calculations that determine how a graphic image actually appears in terms of screen pixels. (The screen consists of rows and 1 columns of small dots, called pixels.) The first transformation A, shears vertically and then compresses each column of pixels; the second transformation A₂ shears horizontally and then stretches each row of pixels. Let A₁ = A₂ = seco 0 0 tano 0 10, and show that the composition of the two transformations is a rotation in 01 Which composition of the transformations represents the rotation? OA. A₁ A₂ OB. A₂A₁ Write the 3x3 matrix that corresponds to the composite transformation. Explain why the composition of the two transformations is a rotation in R². The composition of the two transformations is the transformation matrix in homogeneous coordinates for a (1) O clockwise (1) 1 O counterclockwise (2) O angle 0 000 (Simplify your answers.) O angle p O angle √ O angle ² rotation about the origin at (2) in R². 00 sin cos 0 and 0 01
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:5. A rotation on a computer screen is sometimes implemented as the product of two shear-and-scale transformations, which can speed up calculations that determine how a graphic image actually appears in terms of screen pixels. (The screen consists of rows and
1
columns of small dots, called pixels.) The first transformation A₁ shears vertically and then compresses each column of pixels; the second transformation A₂ shears horizontally and then stretches each row of pixels. Let A₁
=
A₂ =
seco
0
0
tano 0
10
0 1
and show that the composition of the two transformations is a rotation in .
Which composition of the transformations represents the rotation?
O A. A₁ A₂
O B. A₂A₁
Write the 3×3 matrix that corresponds to the composite transformation.
(Simplify your answers.)
Explain why the composition of the two transformations is a rotation in R².
The composition of the two transformations is the transformation matrix in homogeneous coordinates for a (1).
(1)
(2)
clockwise
counterclockwise
angle
1
Φ
angle p
O angle √P
O angle ²
rotation about the origin at (2).
in R².
00
sing cosφ Ο
0
01
and
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