Calculate the concatenated transformation matrix for the following operations performed in the sequence as below: Translation...
Calculate the concatenated transformation matrix for the following operations performed in the sequence as below:
- Translation by 4 and 5 units along X and Y axis
- Change of scale by 2 units in X direction and 4 units in Y direction
iii Rotation by 60° in CCW direction about Z axis passing through the point (4, 4). Find new coordinates when the transformation is carried out on a triangle ABC with A (4, 4), B (8, 4) and C (6, 8).
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Calculate the concatenated transformation matrix for the
following operations performed in the sequence as below:
Translation...
35. Compute the homogeneous transformation representing a translation of 3 units along the r-axis followed by...
35. Compute the homogeneous transformation representing a translation of 3 units along the r-axis followed by a rotation of 3 about the current z-axis followed by a translation of 1 unit along the fixed y-axis. Sketch the frame. What are the coordinates of the origin O1i with respect to the aime in each case
(1 point) Using homogeneous coordinates, the matrix A which reflects the point (5,-4,-1) across t...
(1 point) Using homogeneous coordinates, the matrix A which reflects the point (5,-4,-1) across the x- axis, shifts the result by 1 in the x-direction, -1 in the y-direction, and -1 in the z-direction, and then expands the y coordinate by a factor of 5 is given by A= The image of (5,-4,-1) under this transformation is , and Z =
(1 point) Using homogeneous coordinates, the matrix A which reflects the point (5,-4,-1) across the x- axis, shifts the...
1 point) Using homogeneous coordinates, the matrix A which rotates the point (-4,-5,-1) about the...
1 point) Using homogeneous coordinates, the matrix A which rotates the point (-4,-5,-1) about the z-axis through an angle of counterclockwise as viewed fronm the positive z-axis and then shifts the result by-5 in the x-direction, 4 in the y-direction, and -2 in the z-direction, is given by The image of (-4,-5,-1) under this transformation is 0 , and Z =
1 point) Using homogeneous coordinates, the matrix A which rotates the point (-4,-5,-1) about the z-axis through an angle...
İ need e f and g part thank you for attention Exercise 3.16 In terms of...
İ need e f and g part thank you for attention
Exercise 3.16 In terms of the Xs, ŷs, Zs coordinates of a fixed space frame {s}, frame {a} has its xg-axis pointing in the direction (0,0,1) and its y -axis pointing in the direction (-1,0,0), and frame {b} has its Xb-axis pointing in the direction (1,0,0) and its ýb-axis pointing in the direction (0,0,-1). The origin of {a} is at (3,0,0) in {s} and the origin of {b} is...
A unit cube as shown in Figure Q1 is undergoing the transformations described in (i) and...
A unit cube as shown in Figure Q1 is undergoing the transformations described in (i) and (ii) respectively. Sketch the resultant object with coordinates of each vertex after each transformation. (a) Z (0,1,1) (1,1,1) (0,0,1) (1,0,1) (0,0,0) (1,1,0) (1,0,0) Figure Q1 Transformation (i) (6 marks) 1. A Uniform scale by a factor of 2 2. Followed by a rotation about the-axis in counter-clockwise direction by 90 degrees 3. Followed by a transformation moving in the direction of < 2, 1,...
Question 1: For the plane (2D) truss shown below, evaluate the transformation matrix [T] and the stiffness matrix in the local axis system [KL] of all elements. Use these matrices to evaluate the ele...
Question 1: For the plane (2D) truss shown below, evaluate the transformation matrix [T] and the stiffness matrix in the local axis system [KL] of all elements. Use these matrices to evaluate the element stiffness matrix in global axis system [KG] of the members and assembled them to generate the overall stiffness matrix [K of the truss. Modify the stiffness matrix [K] in order to incorporate boundary conditions following the elimination technique of rows and columns. Take E 200 GPa...
2.1 Summary In this part, you will create a figure, and use linear transformations (matrices) to ...
2.1 Summary In this part, you will create a figure, and use linear transformations (matrices) to move the figure around the screen. In the end, your figure should move up 8 steps, then turn and face left. Reference material for this part can be found in Linear Algebra, and its applications, David Lay, Section 2.7 starting at the beginning of the section up to, but not incluing,3D Graphics. Also, this poster presentation does a pretty good job explaining the same...
1) Assume that a series of experiments are correctly designed and performed. How many are needed...
1) Assume that a series of experiments are correctly designed and performed. How many are needed to disprove a theory? How many are needed to prove a theory? (2) Given the vectors: a = 4 i - 3 j and b = 6 i + 8 j Find the magnitude and direction of: a, b, a + b and a - b (3) A vector has a magnitude of 7.3 units and a direction of 250 degrees (measured counterclockwise from...
For this project, each part will be in its oun matlab script. You will be uploading a total 3 m f...
For this project, each part will be in its oun matlab script. You will be uploading a total 3 m files. Be sure to make your variable names descriptive, and add comments regularly to describe what your code is doing and hou your code aligns with the assignment 1 Iterative Methods: Conjugate Gradient In most software applications, row reduction is rarely used to solve a linear system Ar-b instead, an iterative algorithm like the one presented below is used. 1.1...
Use the following information To help you solve the following questions. Show all work for thumbs...
Use the following information
To help you solve the following questions. Show all
work for thumbs up.
3.1 Rotations and Angular-Momentum Commutation Relations 159 We are particularly interested in an infinitesimal form of Ry: (3.1.4) where terms of order & and higher are ignored. Likewise, we have R0= ° :- R(E) = 1 (3.1.5) and (3.1.5b) - E01 which may be read from (3.1.4) by cyclic permutations of x, y, zthat is, x y , y → 2,2 → x....
35. Compute the homogeneous transformation representing a translation of 3 units along the r-axis followed by a rotation of 3 about the current z-axis followed by a translation of 1 unit along the fixed y-axis. Sketch the frame. What are the coordinates of the origin O1i with respect to the aime in each case
(1 point) Using homogeneous coordinates, the matrix A which reflects the point (5,-4,-1) across the x- axis, shifts the result by 1 in the x-direction, -1 in the y-direction, and -1 in the z-direction, and then expands the y coordinate by a factor of 5 is given by A= The image of (5,-4,-1) under this transformation is , and Z =
(1 point) Using homogeneous coordinates, the matrix A which reflects the point (5,-4,-1) across the x- axis, shifts the...
1 point) Using homogeneous coordinates, the matrix A which rotates the point (-4,-5,-1) about the z-axis through an angle of counterclockwise as viewed fronm the positive z-axis and then shifts the result by-5 in the x-direction, 4 in the y-direction, and -2 in the z-direction, is given by The image of (-4,-5,-1) under this transformation is 0 , and Z =
1 point) Using homogeneous coordinates, the matrix A which rotates the point (-4,-5,-1) about the z-axis through an angle...
İ need e f and g part thank you for attention
Exercise 3.16 In terms of the Xs, ŷs, Zs coordinates of a fixed space frame {s}, frame {a} has its xg-axis pointing in the direction (0,0,1) and its y -axis pointing in the direction (-1,0,0), and frame {b} has its Xb-axis pointing in the direction (1,0,0) and its ýb-axis pointing in the direction (0,0,-1). The origin of {a} is at (3,0,0) in {s} and the origin of {b} is...
A unit cube as shown in Figure Q1 is undergoing the transformations described in (i) and (ii) respectively. Sketch the resultant object with coordinates of each vertex after each transformation. (a) Z (0,1,1) (1,1,1) (0,0,1) (1,0,1) (0,0,0) (1,1,0) (1,0,0) Figure Q1 Transformation (i) (6 marks) 1. A Uniform scale by a factor of 2 2. Followed by a rotation about the-axis in counter-clockwise direction by 90 degrees 3. Followed by a transformation moving in the direction of < 2, 1,...
Question 1: For the plane (2D) truss shown below, evaluate the transformation matrix [T] and the stiffness matrix in the local axis system [KL] of all elements. Use these matrices to evaluate the element stiffness matrix in global axis system [KG] of the members and assembled them to generate the overall stiffness matrix [K of the truss. Modify the stiffness matrix [K] in order to incorporate boundary conditions following the elimination technique of rows and columns. Take E 200 GPa...
2.1 Summary In this part, you will create a figure, and use linear transformations (matrices) to move the figure around the screen. In the end, your figure should move up 8 steps, then turn and face left. Reference material for this part can be found in Linear Algebra, and its applications, David Lay, Section 2.7 starting at the beginning of the section up to, but not incluing,3D Graphics. Also, this poster presentation does a pretty good job explaining the same...
For this project, each part will be in its oun matlab script. You will be uploading a total 3 m files. Be sure to make your variable names descriptive, and add comments regularly to describe what your code is doing and hou your code aligns with the assignment 1 Iterative Methods: Conjugate Gradient In most software applications, row reduction is rarely used to solve a linear system Ar-b instead, an iterative algorithm like the one presented below is used. 1.1...
Use the following information
To help you solve the following questions. Show all
work for thumbs up.
3.1 Rotations and Angular-Momentum Commutation Relations 159 We are particularly interested in an infinitesimal form of Ry: (3.1.4) where terms of order & and higher are ignored. Likewise, we have R0= ° :- R(E) = 1 (3.1.5) and (3.1.5b) - E01 which may be read from (3.1.4) by cyclic permutations of x, y, zthat is, x y , y → 2,2 → x....
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