ellipse pictured below, with semimajor axis of length 3 and at a 30 degree angle with the x-axis, and with and semiminor axis with length 2. Consider the 3. 300 (a) Find a matrix A, that represents a transformation that takes the unit circle to this ellipse. Hint: You may want to think of your transformation as a composition of rotations and scaling. (b) Use the determinant to compute the area of the ellipse. (c) If R is a region of the plane with area equal to 7 units?, what is the area of the image of this region after it undergoes the transformation represented by the matrix 2A?
ellipse pictured below, with semimajor axis of length 3 and at a 30 degree angle with the x-axis, and with and semiminor axis with length 2. Consider the 3. 300 (a) Find a matrix A, that represents a transformation that takes the unit circle to this ellipse. Hint: You may want to think of your transformation as a composition of rotations and scaling. (b) Use the determinant to compute the area of the ellipse. (c) If R is a region of the plane with area equal to 7 units?, what is the area of the image of this region after it undergoes the transformation represented by the matrix 2A?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:1
Consider the
ellipse pictured below, with semimajor axis of length 3 and at a 30 degree angle with
the x-axis, and with and semiminor axis with length 2.
30°
(a) Find a matrix A, that represents
this ellipse. Hint: You may want to think of your transformation as a composition
of rotations and scaling.
transformation that takes the unit circle to
(b) Use the determinant to compute the area of the ellipse.
(c) If R is a region of the plane with area equal to 7 units?, what is the area of
the image of this region after it undergoes the transformation represented by the
matrix 2A?
2
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