Write transformation matrices in order to rotate the point (1,1) on the xy plane by 45 degree counterclockwise with the point (4,5) as the center of rotation. Calculate the coordinates of the rotated point by applying the transformation matrices obtained to the point (1,1).

Q: If R is the rotation matrix, then RRT is a

A: The inverse of a rotation matrix is its transpose, which is also a rotation matrix: The product of…

Q: 6) For the system shown, assume x-y-z is the inertial frame. If the bar first twists around A about…

A: The rotation about z axis is The rotation about x axis is .

Q: 3

A: Given Data : F1= 50 N, Direction 120° F2=30 N, Direction 30°

Q: Find the magnitude and direction of resultant R when A=110N and B=55N, (-2,41 Graphical Solution 1.…

A: Given A=110NB=55NθB=15o

Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

A: To eliminate. The xy- term. Given: The quadratic equation is 8x2-14xy+8y2-42=0.

Q: Write force F2 in vector form

A:

Q: F = 650 N F = 750 N 00 45° F = 900 N F = 50 N 3 F3 = 30 N 15° F2 = 80 N

A:

Q: If the magnitude of the vector is 10m, find (i) The vector format for the shown vector. (ii) The…

A: If the magnitude of the vector is 10m, find (i) The vector format for the shown vector. (ii) The…

Q: For the Scalar projection of F along r = F * Ur How did you get the -41.924 + 24.0327

A: We have following data:Force vector is, Unit vector in the direction of vector r is,

Q: If the coordinate frame 0₁x₁Y₁Z₁ is obtained from the coordinate frame ooxoYoZo by a rotation of /2…

A: Given:The initial frame is represented by The final frame is represented by The first rotation about…

Q: 3 6 4 2 Imaginary Axis -10 -8 -6 -4 -2 0 Real Axis

A:

Q: Write the transformation matrices with its coordinates that you needed to transform figure (5) to…

A: Co-ordinates of the figure are given as:

Q: Assume that the robot is at the position (1, -2, 4), and her right, up, and forward vectors…

A: The position of the robot, The point in the world space,

Q: Find the vector format for vector AB. Find the coordinate angles for AB. 5 ft B7 ft· 10 ft 30⁰ 70°

A: Coordinates of the point  A=(- 10cos70sin30 , 10cos70cos30 , 10sin70) B=(5 , -7 , 0) We need to find…

Q: e. A force acts along a line connecting point 1 ( -14,58,71 ) ft. and point 243,-13,34 ) ft. What is…

A: Step 1: Step 2: Step 3: Step 4:

Q: BF = F,i+ Fj+ F.k a

A:

Q: iven A and b to the​ right, write the augmented matrix for the linear system that corresponds to the…

A: GivenAx=bA=13-3-3-22522b=-714-6

Q: Copy of Based on the kinematic system below If we rotate (A-B) 90 degrees counter-clockwise, and…

A:

Q: 6- if A=L nd B is 3xs unirt matrix A-[ Pind AB)"

A: Given: A=12-13-134-24B=100010001

Q: Calculate the size of projection of vector 1 onto vec Calculate the size of projection of vector 2…

A:

Q: Use the matrix relations to fit a straight line to the data 01234 89431

A: