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(9). In curvilinear coordinates show that the quantity dar druge d-2 transforms as a true vector...
Let D be a 2x2 linear transformation matrix that transforms the vector ? = [ 1...
Let D be a 2x2 linear transformation matrix that transforms the vector ? = [ 1 4 ] into the vector ?? = [ 3 6 ] and transforms the vector ? = [ 2 5 ] into the vector ?? = [ 0 9 ]. Analyze the linear transformation matrix D by doing the following: Let S be a square with side length 2, located in the xy-plane. The matrix D transforms the vertices of S into the vertices...
9. Using Generalized Curvilinear Coördinates, if the scalar S and the vector Ä are both functions...
9. Using Generalized Curvilinear Coördinates, if the scalar S and the vector Ä are both functions of position, prove the following relations: (a) 7 (SA)=s(8. A)+A.IS; (b) (x(SA)=s(0xĂ)+()xA; (c) Ex(s)=0; (a) 8x(0xA)=(. A)-VA. Most of these identities are independent of the specific coördinate system that one employs; however, care must be taken with the operator VA, since in Cartesian Coördinates, it is defined as G?A=i(v?4)+1(v24,)+R(v?4.), but in the Cartesian case, the unit vectors are independent of the coordinate variables, which...
Write the vector differential operator "DEL-V in Cartesian coordinates Cylindrical coordinates Spherical coordinates. 2. Show for...
Write the vector differential operator "DEL-V in Cartesian coordinates Cylindrical coordinates Spherical coordinates. 2. Show for any "nice" scalar function (x,y,z), the Curl of the gradient of (x,y,z) is Zero.. VxVo = 0 Hint: assume the order of differentiation can be switched 3. Find the volume of a sphere of radius R by integrating the infinitesimal volume element of the sphere. 4. Write Maxwell's equations for the case of electro and magneto statics (the fields do not change in time)...
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addi...
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addition, show the unit vectors r, θ, and φ at that point B. Write the vectors ŕ.0, and ф in terms of the unit vectors x, y, and г. Here's the easy way to do this 1. For r, simply use the fact that/r 2. For φ, use the following formula sin θ Explain why the above formula works 3. Compute θ via θ...
U 2 A) 4 d vector space V such that -001 - 402. Find the change-of-coordinates...
U 2 A) 4 d vector space V such that -001 - 402. Find the change-of-coordinates matrix from B to C. B) D) 1 67 1-3-4 For the given matrix and eigenvalue, find an eigenvector corresponding to the eigenvalue. A = -20 612_2 15.09 |-72 22 A) B) 17 C)
2. (True / False) The vector field is irrotational but not incompressible. F(, 9, 2) =...
2. (True / False) The vector field is irrotational but not incompressible. F(, 9, 2) = 2 +y+22) * + y2 +%2' 2 + y2 +2 ,
1 Price vs. quantity Assume that the estimated marginal cost of a technology to purify water...
1 Price vs. quantity Assume that the estimated marginal cost of a technology to purify water is EMC = 2+2q. Assume that the marginal bene?t of one unit of cleaner water is MB = 14?2q. a. What is the estimated optimal quantity of cleaner water? b. What is the estimated optimal price, pe, to pay for one unit of cleaner water? c. Now assume the true marginal cost is MC = 6 + 2q. What is the true optimal quantity...
PLEASE ANSWER ALL PARTS AND SHOW WORK. THANK YOU! If F is a continuous vector field...
PLEASE ANSWER ALL PARTS AND SHOW WORK.
THANK YOU!
If F is a continuous vector field on an oriented surface S with unit normal vector n, then llo F.JS = : Finds Select one: True False Let S be the bottom half of the unit sphere, oriented upward. Let C be the boundary of S, the unit circle in the zy-plane, oriented counterclockwise as viewed from above. Then for any vector field F with continuous first-order partial derivatives, SP.d -...
True or False Determine whet her the statement is true or false, and circle the correct answer. Each question is worth 2 points. (1) If F is a vector field and C is an oriented curve, then F dr must...
True or False Determine whet her the statement is true or false, and circle the correct answer. Each question is worth 2 points. (1) If F is a vector field and C is an oriented curve, then F dr must be less than zero. F (2) It is possible that for a certain vector field F and piecewise smooth oriented path C we have/. F. dr-2i-Sj. (3) Suppose d·is the unit square joining the points (0,0), (1,0), (1,1), (0.1) oriented...
2. Find the force (vector) between Q1-40uC r1 (x1-2,y1-2,z1-3) and Q2-47uCr2 (x2-3,y2-3,z2-1) A) .68i 34j -69k B) 1.25 .62j-1.26k 12 0 Fi C) 1.44i .72-145k D) 1.06i .53j-1.07k 5. When the coordinates...
2. Find the force (vector) between Q1-40uC r1 (x1-2,y1-2,z1-3) and Q2-47uCr2 (x2-3,y2-3,z2-1) A) .68i 34j -69k B) 1.25 .62j-1.26k 12 0 Fi C) 1.44i .72-145k D) 1.06i .53j-1.07k 5. When the coordinates of a system don't have components over the coordinates, we determine that they are D. Rectangular A. Orthogonal C. Inclusive 7. A vector V1 (x=4, y-6, z-8), which is the magnitude of the projection on the YZ plane A) 10 X 1 V 1 B) 8.5 C 13...
9. Using Generalized Curvilinear Coördinates, if the scalar S and the vector Ä are both functions of position, prove the following relations: (a) 7 (SA)=s(8. A)+A.IS; (b) (x(SA)=s(0xĂ)+()xA; (c) Ex(s)=0; (a) 8x(0xA)=(. A)-VA. Most of these identities are independent of the specific coördinate system that one employs; however, care must be taken with the operator VA, since in Cartesian Coördinates, it is defined as G?A=i(v?4)+1(v24,)+R(v?4.), but in the Cartesian case, the unit vectors are independent of the coordinate variables, which...
Write the vector differential operator "DEL-V in Cartesian coordinates Cylindrical coordinates Spherical coordinates. 2. Show for any "nice" scalar function (x,y,z), the Curl of the gradient of (x,y,z) is Zero.. VxVo = 0 Hint: assume the order of differentiation can be switched 3. Find the volume of a sphere of radius R by integrating the infinitesimal volume element of the sphere. 4. Write Maxwell's equations for the case of electro and magneto statics (the fields do not change in time)...
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addition, show the unit vectors r, θ, and φ at that point B. Write the vectors ŕ.0, and ф in terms of the unit vectors x, y, and г. Here's the easy way to do this 1. For r, simply use the fact that/r 2. For φ, use the following formula sin θ Explain why the above formula works 3. Compute θ via θ...
U 2 A) 4 d vector space V such that -001 - 402. Find the change-of-coordinates matrix from B to C. B) D) 1 67 1-3-4 For the given matrix and eigenvalue, find an eigenvector corresponding to the eigenvalue. A = -20 612_2 15.09 |-72 22 A) B) 17 C)
2. (True / False) The vector field is irrotational but not incompressible. F(, 9, 2) = 2 +y+22) * + y2 +%2' 2 + y2 +2 ,
PLEASE ANSWER ALL PARTS AND SHOW WORK.
THANK YOU!
If F is a continuous vector field on an oriented surface S with unit normal vector n, then llo F.JS = : Finds Select one: True False Let S be the bottom half of the unit sphere, oriented upward. Let C be the boundary of S, the unit circle in the zy-plane, oriented counterclockwise as viewed from above. Then for any vector field F with continuous first-order partial derivatives, SP.d -...
True or False Determine whet her the statement is true or false, and circle the correct answer. Each question is worth 2 points. (1) If F is a vector field and C is an oriented curve, then F dr must be less than zero. F (2) It is possible that for a certain vector field F and piecewise smooth oriented path C we have/. F. dr-2i-Sj. (3) Suppose d·is the unit square joining the points (0,0), (1,0), (1,1), (0.1) oriented...
2. Find the force (vector) between Q1-40uC r1 (x1-2,y1-2,z1-3) and Q2-47uCr2 (x2-3,y2-3,z2-1) A) .68i 34j -69k B) 1.25 .62j-1.26k 12 0 Fi C) 1.44i .72-145k D) 1.06i .53j-1.07k 5. When the coordinates of a system don't have components over the coordinates, we determine that they are D. Rectangular A. Orthogonal C. Inclusive 7. A vector V1 (x=4, y-6, z-8), which is the magnitude of the projection on the YZ plane A) 10 X 1 V 1 B) 8.5 C 13...
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