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(1 pt) The vector u = vrx + vyy in a two-dimensional xy-space is of length...
please help me with questions 1，2，3 1. Let V be a 2-dimensional vector space with basis...
please help me with questions 1，2，3
1. Let V be a 2-dimensional vector space with basis X = {v1, v2}, write down the matrices [0]xx and [id]xx. 2. Let U, V, W be vector spaces and S:U +V, T:V + W be linear transforma- tions. Define the composition TOS:U + W by To S(u) = T(S(u)) for all u in U. a. Show that ToS is a linear transformation. b. Now suppose U is 1-dimensional with basis X {41}, V...
QUESTION 1 A quantity, 7", in an n-dimensional space that has n values and transforms between...
QUESTION 1 A quantity, 7", in an n-dimensional space that has n values and transforms between reference frames S and S in the same way as an infinitesimal displacement (dx), that is: is called a contravariant vector Let T be a contravariant vector in a 2-dimensional space, and let S be defined in Sas: 4 and 12 with A = 3 and B = -2 Find the second component, 7", of the vector in S, at point P, where the...
(1 point) Consider the two dimensional subspace U of R* spanned by the set {u1, u2}...
(1 point) Consider the two dimensional subspace U of R* spanned by the set {u1, u2} where [1] u = T 37 -1 1-3] U2 = 3 : The orthogonal complement V = Ut of U ER is the one dimensional subspace of Rº such that every vector ve V is orthogonal to every vector ue U. In other words, u: v=0 for all ue U and ve V. Find the first two components V1 and 12 of the vector...
2. Consider a three-dimensional Universe. A vector of this space, starts from the origin of the...
2. Consider a three-dimensional Universe. A vector of this space, starts from the origin of the coordinate system and has the tip described by the coordinates 1, 0, a) Write the matrix that describes a rotation of this three dimensional vector about the Oz axis by an angle of 45° Both the initial and the final coordinates have the same origin. b) Calculate the projections (of the tip) of this vector along the new axes of coordinates.
Consider the following region and the vector field F. a. Compute the two-dimensional divergence of the...
Consider the following region and the vector field F. a. Compute the two-dimensional divergence of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency F= (2x-2y); R=(x,y): x2 + y²59 a. The two-dimensional divergence is (Type an exact answer.) b. Set up the integral over the region. Write the integral using polar coordinates with r as the radius and O as the angle SO rdr d0 (Type exact answers.) 0 o Set up the line...
Consider a two-dimensional state vector space and a basis in this space lay), laz), eigenvectors of...
Consider a two-dimensional state vector space and a basis in this space lay), laz), eigenvectors of an observable A: Ala) = aja) Alaz) = azlaz) A representation of Hamiltonian operator in this basis is: H = (8 5) Find: -Eigenstates and eigenvalues of H. -If the system is in state |az) at time t=0, What is the state vector of the system at time t? -What is the probability of finding the system in the state |az) at time t?...
Two vectors, r and vector s lie in the xy plane. Their magnitudes are 4.26 and 7.75...
Two vectors, r and vector s lie in the xy plane. Their magnitudes are 4.26 and 7.75 units, respectively, and their directions are 345o and 63.0o, respectively, as measured counterclockwise from the positive x axis. What are the values of (a) vector r ⋅ vector s and (b) | vector r × vector s |? show units
7. [2p] (a) In a two-dimensional linear space X vectors el, e2 formi a basis. In this basis a vector r E X has expansio...
7. [2p] (a) In a two-dimensional linear space X vectors el, e2 formi a basis. In this basis a vector r E X has expansion x = 2e1 + e2. Find expansion of the vector x in another basis 1 -2 er, e2, of X, if the change of basis matrix from the basis e to the basis e, s (b) In a two-dimensional linear space X vectors el, e2 forn a basis. In this basis a vector r E...
A two-dimensional vector has an x-component of 5.06 meters and a y-component of 9.18 meters. Calculate...
A two-dimensional vector has an x-component of 5.06 meters and a y-component of 9.18 meters. Calculate the magnitude of this two-dimensional vector 1.067 meters 1,067 meters CHECK ANSWER 1 of 2 attempts used LAST ATTEMPT Question5 A two-dimensional vector has an x-component of 8.95 meters and a y-component of 3.33 meters. Calculate the angle (in degrees) that this two-dimensional vector makes with the positive x-axis Enter answer here : degrees of 2 attempts used CHECK ANSWER Question 6 A two-dimensional...
MW 08:00-09:15 PHY 2053 Test #1 2019-01-30 3. In the figure below, vector A has a...
MW 08:00-09:15 PHY 2053 Test #1 2019-01-30 3. In the figure below, vector A has a magnitude of 15.00 m measured from the negative x-axis, angle of θ straight down. directed at an angle θ,-25° vector B has a magnitude of 10.45 m directed at an from the negative x-acis, and vector C has a magnitude of 8.45 ml directed B 12 (a) Find the x-and y-components of vector A (b) Find the x- and y-components of vector B (c)...
please help me with questions 1，2，3
1. Let V be a 2-dimensional vector space with basis X = {v1, v2}, write down the matrices [0]xx and [id]xx. 2. Let U, V, W be vector spaces and S:U +V, T:V + W be linear transforma- tions. Define the composition TOS:U + W by To S(u) = T(S(u)) for all u in U. a. Show that ToS is a linear transformation. b. Now suppose U is 1-dimensional with basis X {41}, V...
QUESTION 1 A quantity, 7", in an n-dimensional space that has n values and transforms between reference frames S and S in the same way as an infinitesimal displacement (dx), that is: is called a contravariant vector Let T be a contravariant vector in a 2-dimensional space, and let S be defined in Sas: 4 and 12 with A = 3 and B = -2 Find the second component, 7", of the vector in S, at point P, where the...
(1 point) Consider the two dimensional subspace U of R* spanned by the set {u1, u2} where [1] u = T 37 -1 1-3] U2 = 3 : The orthogonal complement V = Ut of U ER is the one dimensional subspace of Rº such that every vector ve V is orthogonal to every vector ue U. In other words, u: v=0 for all ue U and ve V. Find the first two components V1 and 12 of the vector...
2. Consider a three-dimensional Universe. A vector of this space, starts from the origin of the coordinate system and has the tip described by the coordinates 1, 0, a) Write the matrix that describes a rotation of this three dimensional vector about the Oz axis by an angle of 45° Both the initial and the final coordinates have the same origin. b) Calculate the projections (of the tip) of this vector along the new axes of coordinates.
Consider the following region and the vector field F. a. Compute the two-dimensional divergence of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency F= (2x-2y); R=(x,y): x2 + y²59 a. The two-dimensional divergence is (Type an exact answer.) b. Set up the integral over the region. Write the integral using polar coordinates with r as the radius and O as the angle SO rdr d0 (Type exact answers.) 0 o Set up the line...
Consider a two-dimensional state vector space and a basis in this space lay), laz), eigenvectors of an observable A: Ala) = aja) Alaz) = azlaz) A representation of Hamiltonian operator in this basis is: H = (8 5) Find: -Eigenstates and eigenvalues of H. -If the system is in state |az) at time t=0, What is the state vector of the system at time t? -What is the probability of finding the system in the state |az) at time t?...
7. [2p] (a) In a two-dimensional linear space X vectors el, e2 formi a basis. In this basis a vector r E X has expansion x = 2e1 + e2. Find expansion of the vector x in another basis 1 -2 er, e2, of X, if the change of basis matrix from the basis e to the basis e, s (b) In a two-dimensional linear space X vectors el, e2 forn a basis. In this basis a vector r E...
A two-dimensional vector has an x-component of 5.06 meters and a y-component of 9.18 meters. Calculate the magnitude of this two-dimensional vector 1.067 meters 1,067 meters CHECK ANSWER 1 of 2 attempts used LAST ATTEMPT Question5 A two-dimensional vector has an x-component of 8.95 meters and a y-component of 3.33 meters. Calculate the angle (in degrees) that this two-dimensional vector makes with the positive x-axis Enter answer here : degrees of 2 attempts used CHECK ANSWER Question 6 A two-dimensional...
MW 08:00-09:15 PHY 2053 Test #1 2019-01-30 3. In the figure below, vector A has a magnitude of 15.00 m measured from the negative x-axis, angle of θ straight down. directed at an angle θ,-25° vector B has a magnitude of 10.45 m directed at an from the negative x-acis, and vector C has a magnitude of 8.45 ml directed B 12 (a) Find the x-and y-components of vector A (b) Find the x- and y-components of vector B (c)...
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