Describe a deformation of the (x, y) plane. Find the matrix C which diagonalizes M and the matrix D which gives the deformation relative to the new axes.

Q: What is the cross product A x B? Find the x component. Find the y component.

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Q: Find the coordinates of the centroid of the homogeneous plate OPBA shown in Figure Q3.c. The plate…

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Q: Discuss about the Matrix Systems?  Please answer at your own words.

A: The matrix system in the field of the physics is useful in the case of the multiple thick lenses.…

Q: On more than two vectors. The first has a standard of 11m/s, the other a standard of 3m/s. All…

A: Given, resultant of vector A(say) = 11m/s resultant of vector B(say) = 3m/s So, sum of these two…

Q: Which among the following is the distributive law for the cross product of three vectors? a)…

A: Option a

Q: A curve in three dimensional space is parametrized as F(u) = cos(u)i + sin(u)j + cos(3u)k, и є [0,…

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Q: Add a third cable to this diagram originating at point A and extending up to the wall that B and C…

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Q: Consider the following force vectors: A = -3î + j + 2k (N) B = 2î – } – k (N) 1. Vectors Á, B, and C…

A: The given vectors, A→=-3i^+j^+2k^B→=2i^-j^-k^

Q: AB- AB sine, where @ is the angle between the two vectors

A: Remember the vector law and formulas

Q: The two forces shown act on the structural member AB. Determine the magnitude of P (N) if Q=3885N…

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Q: Given a vector (77, 48, 22) and another vector (4, 49, 67) what is the z-component of their sum?

A: Given that Vector 1 (A)= (77, 48, 22)  And , vector 2 (B)= (4, 49, 67) Let i, j and k be the unit…

Q: Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to…

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Q: Pole AB is fixed to a wall at Point B. The pole is subjected to a force F at Point A. If the…

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Q: The 3X3 matrix which is being made is having axis coordinates, point coordinates and the force…

A: Axis coordinates, point coordinates, and the force coordinates

Q: The given truss below is loaded vertically downward with 4KN and 8KN at points C and D,…

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Q: Write down an expression for the net force on a simple pendulum of the mass malong (tangentially to)…

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Q: Determine the magnitude of the following cross product: ( 11 7 +57 ) X (27 +57)

A: Given: The vectors are 11i+5j and 2i+5j

Q: The given truss below is loaded vertically downward with 4KN and 8KN at points C and D,…

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Q: b) Convert the vector A= - ax at P(0,2,0) to cylinderical coordinat system.

A: The cylindrical coordinate system (r,φ,z) is shown below:   The transformation between cylindrical…

Q: Define the cross product of two(2) vectors on a plane and describe their application with respect to…

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Q: Problems 3-1. Add the force vectors F=(21.31-9.5) N and F₂ = (10.71 +5.23) N quantitatively and…

A: The objective of this question is to add two force vectors both quantitatively and graphically. The…

Q: Multiply the Following Vectors using cross Product method. W = ř x F F = ( 5i + 3j – 8 k) N * = (2i…

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Q: Vector Å has magnitude of 6 units and is in the direction of the +x-axis. Vector B has a magnitude…

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Q: 7. YA 60° A = 10.0 30 B 30° 53° D = 20.0 37° C = 12.0 10 F = 20.0 B = 5.0

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Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: Solution:-

Q: Consider three vectors: What is the result of 2A. (B-3C)? ) What is the result of A A+B B+C. C? . A…

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Q: Consider the following 2D vector given in component form v = (5.8,7.2). At what angle is this vector…

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Q: If the density at any point is given by. p=k√x² + y² Determine the mass of the solid bounded by the…

A: Given: The density function ρ=kx2+y2 bounded Surface z=xyx=1;y=1;z=0

Q: The density of a spherical solid at a point P = (x, y, z) is given by f(x, y, z) = c(x² + y² + z²) ,…

A: The density of spherical solid at any point P(x,y,z) is given by,  Therefore, the density at point…

Q: Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to…

A: Let F1, F2, and F­3 denote the three forces, θ1, θ2, and θ3 denote the three angles of the forces…

Q: A vector field is given in spherical coordinates as B=RR² cos(6/2) + Rsin(0) sin(0/2) . Evaluate (V…

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Q: Problem # 01: Given two vectors u and v, the dot product (also called inner product) is defined by…

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Q: A: Given the vectors a=i-2 j+3k and b=-2i+3j-k, show that the cross product ax b is orthogonal to…

A: Two vectors are orthogonal to each other if the dot product between them is equal to zero. i.e,…

Q: a. Prove the triple product identity Ax(BxC)= B(AC)-C(A.B).

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Q: Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to…

A: Given: The resultant magnitude R and the angle θ between the x-axis and the line of action of the…

Q: Describe 2-dimentional vector addition for any scenario? Put your bes example over here.

A: Vector addition in two dimension Let us consider two vectors A →and B→, such that they are oriented…

Q: Two structural members A and B are bolted to a bracket as shown. Knowing that both members are in…

A: Given-Compression force in A, Compression force in B, Free Body Diagram -

Q: Consider the gusset plate of a bridge truss shown in ( Figure 1). Suppose that F₁ = 8 kN. F₂ = 6 kN.…

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Q: The uniform 14-m pole has a mass of 130 kg and is supported by its smooth ends against the vertical…

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