Vector B,(r) (so in the B system) is (1,1,1). What are the coordinates of N,(r) when...
Vector B,(r) (so in the B system) is (1,1,1). What are the coordinates of N,(r) when is given that system B is gained by rotating system N with positive angle (.25)pi around the y-as?
Answer is: sqr(2),1,0. How?
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Vector B,(r) (so in the B system) is (1,1,1). What are the
coordinates of N,(r) when...
Part A. Geometric Addition What is the magnitude and direction of the resultant vector, R, when...
Part A. Geometric Addition
What is the magnitude and direction of the resultant vector, R,
when the parallelogram law is applied to A and B?
Part B. Component addition of vectors
What is the resultant vector, R, obtained by adding vectors C
and D?
Part C. Addition of more than two vectors
For the vector sum R = A + B + C + D, what are the magnitude and
direction of the resultant R?
Learning Goal: To use geometric...
1. (25 pts) Given integer N > 0; vector r of distinct nodes with N components,...
1. (25 pts) Given integer N > 0; vector r of distinct nodes with N components, ordered from smallest to largest; vector y of nonzero values at nodes with N components suppose the piecewise linear interpolant P(x) of this data has a root. Complete the Matlab function with header function [root] linearinterpolationroot(N,x.y) so that it outputs the smallest root of P(r). Remember, the piecewise linear interpolant is only defined between the smallest and largest nodes.
1. (25 pts) Given integer...
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the...
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the...
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
Consider a vector field given in cartesian coordinates (r, y,2) by uy (A) Calculate the curl...
Consider a vector field given in cartesian coordinates (r, y,2) by uy (A) Calculate the curl of this vector field ▽ ˇ (B) Verify that Stokes theorem holds if the contour is the square with corners (d, d, 0), (-d, d, 0), ( d, d, 0), and (d,-d,0) aid the surface spanned by this (ont our is at 0.
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...
D. Vector D has a magnitude of 59 N and an angle θ of 39°. What...
D. Vector D has a magnitude of 59 N and an angle θ of 39°. What is the x-component of vector D? (include units with answer) A vector has an x-component of 15.0 m/s and a y-component of-5.0 m/s Determine the magnitude of the vector. (include units with answer) E. What is the angle of the vector of Part E measured counterclockwise (CCW) from the positive x-axis? Answer must within 0.5 degrees (include units with answer) F. A vector has...
A system is given by y(n + 1)-ay(n) + bc(n), where a and b are unknown. When y(0) 1,c(n) 0 for n
A system is given by y(n + 1)-ay(n) + bc(n), where a and b are unknown. When y(0) 1,c(n) 0 for n <0 and c(n) - 1 for n 2 0, it is known that y(1) 0.5, y(2) 1.25, y(3) 1.625, y(4) 1.8125, and y(5) 1.90625. Use direct adaptive control to generate c (3), c(4), and c(5) for tracking the reference r(n)-1. Express your answer by giving the equation for the control values c(3),c(4), and c(5)
A system is given...
LE 4) (Ungraded) In Cartesian coordinates, the curl of a vector field Air) is defined as...
LE 4) (Ungraded) In Cartesian coordinates, the curl of a vector field Air) is defined as Use the definition of electric potential to find the potential difference between the origin and r = x + y + 27, V(r) - V(O) = - Ed. As the line integral is independent of path, choose whatever path you find to be con- vertient Taking V(0) = 0, what is V(r)? Finally, confirm that taking the gradient of the potential recovers our original...
1 Cylindrical coordinate system Given the relation of the cylindrical coordinate system r=r cos pi+r sin...
1 Cylindrical coordinate system Given the relation of the cylindrical coordinate system r=r cos pi+r sin øj + zk (1) Lets define vectors er, eg, and ez, that indicate the direction of the vectors in the cylindrical coordinate system. Using the definition ar e = pt=r, p2 = 0, p3 (2) (a) Find a matrix for calculating er, er and e, in terms of i, j, and k. Invert the relation for expressing i, j, and k in terms of...
Part A. Geometric Addition
What is the magnitude and direction of the resultant vector, R,
when the parallelogram law is applied to A and B?
Part B. Component addition of vectors
What is the resultant vector, R, obtained by adding vectors C
and D?
Part C. Addition of more than two vectors
For the vector sum R = A + B + C + D, what are the magnitude and
direction of the resultant R?
Learning Goal: To use geometric...
1. (25 pts) Given integer N > 0; vector r of distinct nodes with N components, ordered from smallest to largest; vector y of nonzero values at nodes with N components suppose the piecewise linear interpolant P(x) of this data has a root. Complete the Matlab function with header function [root] linearinterpolationroot(N,x.y) so that it outputs the smallest root of P(r). Remember, the piecewise linear interpolant is only defined between the smallest and largest nodes.
1. (25 pts) Given integer...
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
Consider a vector field given in cartesian coordinates (r, y,2) by uy (A) Calculate the curl of this vector field ▽ ˇ (B) Verify that Stokes theorem holds if the contour is the square with corners (d, d, 0), (-d, d, 0), ( d, d, 0), and (d,-d,0) aid the surface spanned by this (ont our is at 0.
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...
D. Vector D has a magnitude of 59 N and an angle θ of 39°. What is the x-component of vector D? (include units with answer) A vector has an x-component of 15.0 m/s and a y-component of-5.0 m/s Determine the magnitude of the vector. (include units with answer) E. What is the angle of the vector of Part E measured counterclockwise (CCW) from the positive x-axis? Answer must within 0.5 degrees (include units with answer) F. A vector has...
A system is given by y(n + 1)-ay(n) + bc(n), where a and b are unknown. When y(0) 1,c(n) 0 for n <0 and c(n) - 1 for n 2 0, it is known that y(1) 0.5, y(2) 1.25, y(3) 1.625, y(4) 1.8125, and y(5) 1.90625. Use direct adaptive control to generate c (3), c(4), and c(5) for tracking the reference r(n)-1. Express your answer by giving the equation for the control values c(3),c(4), and c(5)
A system is given...
LE 4) (Ungraded) In Cartesian coordinates, the curl of a vector field Air) is defined as Use the definition of electric potential to find the potential difference between the origin and r = x + y + 27, V(r) - V(O) = - Ed. As the line integral is independent of path, choose whatever path you find to be con- vertient Taking V(0) = 0, what is V(r)? Finally, confirm that taking the gradient of the potential recovers our original...
1 Cylindrical coordinate system Given the relation of the cylindrical coordinate system r=r cos pi+r sin øj + zk (1) Lets define vectors er, eg, and ez, that indicate the direction of the vectors in the cylindrical coordinate system. Using the definition ar e = pt=r, p2 = 0, p3 (2) (a) Find a matrix for calculating er, er and e, in terms of i, j, and k. Invert the relation for expressing i, j, and k in terms of...
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