![(c) [1 point] Let R : E3 → E3 be the rotation in E3 with axis in the direction of the vector ã=(-1,2, -2) and angle 0 = . If](http://img.homeworklib.com/questions/f6af3490-4cf5-11eb-8acd-8bdc6492c399.png?x-oss-process=image/resize,w_560)
Homework Answers
(1 point) Match each linear transformation with its matrix. A. Contraction by a factor of2 B. Rotation through an angle of 90 in the clockwise direction C. Projection onto the y-axis D. Reflection in...
(1 point) Match each linear transformation with its matrix. A. Contraction by a factor of2 B. Rotation through an angle of 90 in the clockwise direction C. Projection onto the y-axis D. Reflection in the y-axis E. Rotation through an angle of 90° in the counterclockwise direction -1 0 0.5 0 0 0.5 0 -1 F. Reflection in the r-axis 0 -1
(1 point) Match each linear transformation with its matrix. A. Contraction by a factor of2 B. Rotation through...
please provide clear drawings for each 5. Let T9,b) (x, y) = (x +a, y +b)...
please provide clear drawings for each
5. Let T9,b) (x, y) = (x +a, y +b) and Rę be the reflection about a line l. a. T<1.2> Rc=y (3,5) = b. Rc=yo T<1,2> (3,5) = c. If P is the point (2,1), find the image of P: under the reflection R-axis: under R2=3: under the half turn Riso about the origin: under the half turn R180 about the center (1,1).
(4) (a) Determine the standard matrix A for the rotation r of R 3 around the z-axis through the a...
(4) (a) Determine the standard matrix A for the rotation r of R
3 around the z-axis through the angle π/3 counterclockwise. Hint:
Use the matrix for the rotation around the origin in R 2 for the
xy-plane. (b) Consider the rotation s of R 3 around the line
spanned by h 1 2 3 i through the angle π/3 counterclockwise. Find a
basis of R 3 for which the matrix [s]B,B is equal to A from (a).
(c) Give...
(1 point) Let C be a semicircle of radius r> 0 centered at the origin. Let...
(1 point) Let C be a semicircle of radius r> 0 centered at the origin. Let P be a point on the x-axis whose coordinates are P= (r + rt, 0) where t> 0. Let L be a line through P which is tangent to the semicircle. Let A denote the triangular region between the circle and the line and above the x-axis (see figure.) (Click on image for a larger view) MON Find the exact area of A in...
4. Let l be the line through the origin which has a directed) angle of inclination...
4. Let l be the line through the origin which has a directed) angle of inclination 8 from positive x-axis. Let l' be the line through h + Oi with (directed) angle of inclination from positive c-axis. (a) Use re = ROTOR_, to derive the complex equation for the reflection re(2). (b) Use part (a) and re = T re(2) reo T-to derive the complex equation of the reflection
In Problems 1-9, consider the given vector x. Find the vectors that result from each of the follo...
1,5
In Problems 1-9, consider the given vector x. Find the vectors that result from each of the following: (a) stretch by a factor of c (sketch the original vector and the resulting vector) (b) rotation by an angle of ф (sketch the original vector, the angle of rotation, 716 Appendix B. Selected Topics from Linear Algebra and the resulting vector) original vector, the line of projection, and the resulting vector) the original vector, the line of reflection, and the...
In R2 let R be the rotation about the origin through the angle 27/14. Then the...
In R2 let R be the rotation about the origin through the angle 27/14. Then the matrix [R] representing Ris [R] = Consequently R transforms the point (1, 2) into Check
a) Let L be the line through (2,-1,1) and (3,2,2). Parameterize L. Find the point Q...
a) Let L be the line through (2,-1,1) and (3,2,2). Parameterize L. Find the point Q where L intersects the xy-plane. b) Find the angle that the line through (0,-1,1) and (√3,1,4) makes with a normal vector to the xy-plane. c) Find the distance from the point (3,1,-2) to the plane x-2y+z=4. d) Find a Cartesian equation for the plane containing (1,1,2), (2,1,1) and (1,2,1)
Problem: Given a rotation R of R3 about an arbitrary axis through a given angle find the matrix w...
Problem: Given a rotation R of R3 about an arbitrary axis through a given angle find the matrix which represents R with respect to standard coordinates. Here are the details: The axis of rotation is the line L, spanned and oriented by the vector v (1,一1,-1) . Now rotate R3 about L through the angle t = 4 π according to the Right 3 Hand Rule Solution strategy: If we choose a right handed ordered ONB B- (a, b,r) for...
5. (3) Let X = Serie x = ()m - (*) indo 3 x 3 mais...
5. (3) Let X = Serie x = ()m - (*) indo 3 x 3 mais Find a 3 x 3 matrix A such that the projection PAX = e vector X ER projected onto the line I that is parallel to a and passes through the origin. Pex - Ax 6. (4) The line l in Ris given by the equation x + 3y = 0. (a) What is the angle e between the positive x-axis and the line...
(1 point) Match each linear transformation with its matrix. A. Contraction by a factor of2 B. Rotation through an angle of 90 in the clockwise direction C. Projection onto the y-axis D. Reflection in the y-axis E. Rotation through an angle of 90° in the counterclockwise direction -1 0 0.5 0 0 0.5 0 -1 F. Reflection in the r-axis 0 -1
(1 point) Match each linear transformation with its matrix. A. Contraction by a factor of2 B. Rotation through...
please provide clear drawings for each
5. Let T9,b) (x, y) = (x +a, y +b) and Rę be the reflection about a line l. a. T<1.2> Rc=y (3,5) = b. Rc=yo T<1,2> (3,5) = c. If P is the point (2,1), find the image of P: under the reflection R-axis: under R2=3: under the half turn Riso about the origin: under the half turn R180 about the center (1,1).
(4) (a) Determine the standard matrix A for the rotation r of R
3 around the z-axis through the angle π/3 counterclockwise. Hint:
Use the matrix for the rotation around the origin in R 2 for the
xy-plane. (b) Consider the rotation s of R 3 around the line
spanned by h 1 2 3 i through the angle π/3 counterclockwise. Find a
basis of R 3 for which the matrix [s]B,B is equal to A from (a).
(c) Give...
(1 point) Let C be a semicircle of radius r> 0 centered at the origin. Let P be a point on the x-axis whose coordinates are P= (r + rt, 0) where t> 0. Let L be a line through P which is tangent to the semicircle. Let A denote the triangular region between the circle and the line and above the x-axis (see figure.) (Click on image for a larger view) MON Find the exact area of A in...
4. Let l be the line through the origin which has a directed) angle of inclination 8 from positive x-axis. Let l' be the line through h + Oi with (directed) angle of inclination from positive c-axis. (a) Use re = ROTOR_, to derive the complex equation for the reflection re(2). (b) Use part (a) and re = T re(2) reo T-to derive the complex equation of the reflection
1,5
In Problems 1-9, consider the given vector x. Find the vectors that result from each of the following: (a) stretch by a factor of c (sketch the original vector and the resulting vector) (b) rotation by an angle of ф (sketch the original vector, the angle of rotation, 716 Appendix B. Selected Topics from Linear Algebra and the resulting vector) original vector, the line of projection, and the resulting vector) the original vector, the line of reflection, and the...
In R2 let R be the rotation about the origin through the angle 27/14. Then the matrix [R] representing Ris [R] = Consequently R transforms the point (1, 2) into Check
Problem: Given a rotation R of R3 about an arbitrary axis through a given angle find the matrix which represents R with respect to standard coordinates. Here are the details: The axis of rotation is the line L, spanned and oriented by the vector v (1,一1,-1) . Now rotate R3 about L through the angle t = 4 π according to the Right 3 Hand Rule Solution strategy: If we choose a right handed ordered ONB B- (a, b,r) for...
5. (3) Let X = Serie x = ()m - (*) indo 3 x 3 mais Find a 3 x 3 matrix A such that the projection PAX = e vector X ER projected onto the line I that is parallel to a and passes through the origin. Pex - Ax 6. (4) The line l in Ris given by the equation x + 3y = 0. (a) What is the angle e between the positive x-axis and the line...
Most questions answered within 3 hours.
-
Investor company owns 35% of investee company voting stock and
accounts for the investment under the...
asked 34 minutes ago -
The number of major faults on a randomly chosen 1 km stretch of
highway has a...
asked 59 minutes ago -
Consider the competitive environment of Starbuck's, Progressive
Insurance, a manufacturing firm with low turnover, or a...
asked 1 hour ago -
3. Gains from trade
Consider two neighbouring island countries called Euphoria and
Contente. They each have...
asked 3 hours ago -
A business executive has the option to invest money in two
plans: Plan A guarantees that...
asked 6 hours ago -
Hello, can someone please help me answer this question?
How much heat is absorbed by a...
asked 5 hours ago -
. A marketing researcher conducted a survey of 25 shoppers
randomly selected at the local mall...
asked 6 hours ago -
Create an comprehensive response to the
following:
Antimicrobial agents work on a multitude of microbes (bacteria,...
asked 6 hours ago -
6.13 LAB: Step counter. Section 6.3.
A pedometer treats walking 2,000 steps as walking 1 mile....
asked 6 hours ago -
(14.2) A block of mass m = 10 kg riding on a frictionless
horizontal plane is...
asked 6 hours ago -
Use any search engine to search for articles about Starbucks
partnership with Tata Companies in India...
asked 6 hours ago -
Let’s say that for some reason Bank Excess Reserves suddenly
increase sharply. What effect would this...
asked 6 hours ago