Questions and Answers of An Introduction To Accounting 1st

Considering only u, d, s, and c, how many different neutral mesons are possible?
The quark content of $\pi^{+}$is $u \bar{d}$. Based on this, what is the quark content of $\pi^{-}$?
The $\Lambda^{0}$ particle can be produced in pion-nucleon collisions according to the reaction\[\pi^{-}+p^{+} ightarrow \Lambda^{0}+K^{0}\]Show that the conservation laws for electric charge,
$\mu$-decays according to\[\mu^{-} ightarrow e^{-}+v_{\mu}+\bar{v}_{e}\]Show that the conservation laws for electric charge, baryon number, and lepton number are all satisfied.
The decay\[\Xi^{-} ightarrow \Sigma^{-}+\pi^{\circ}\]proceeds only by the weak interaction. What conservation law prevents decay by the strong interaction?
The decay\[\Lambda^{0} ightarrow p^{+}+\pi^{-}\]proceeds only by the weak interaction. What conservation law prevents decay by the strong interaction?
Evaluate $\mathbf{T} e^{x}$ for the transformation $\mathbf{T} x=-x$.
Evaluate $\mathbf{T} \cos x$ for the transformation $\mathbf{T} x=-x$.
Express the inverse $(\mathbf{A B})^{-1}$ of the product $\mathbf{A B}$ in terms of $\mathbf{A}$ and $\mathbf{B}$.
Show that the positive and negative real integers (including 0) form a group under the operation of addition.
Show that the real integers $1,2, \ldots$ do not form a group under the operation of multiplication.
Show that the group members $\{\mathbf{E}, \mathbf{A}, \mathbf{B}\}$ for the 3-fold rotation of an equilateral triangle. can be written $\left\{\mathbf{E}, \mathbf{B}, \mathbf{B}^{2}ight\}$.
Write the product table for a group of order 2.
Write a product table for the 4-fold rotations of a square about its geometric center. Is this a cyclic group? E: rotate by 0 A: rotate by 90 B: rotate by 180 C: rotate by 270
Prove that a given group member occurs only once in a given column of the product table.
Cayley proved that every discrete group of order $n$ can be found in the product table for $S_{n}$. Illustrate this result for $S_{3}$ (Table 1.5 or Table 1.6). What does your result say about
There are only two distinct groups of order 4. One of them is the group for rotations of a square, Problem 8 . Here is the product table of the other.Show that \(\{\mathbf{E}, \mathbf{K}, \mathbf{L},
Find three subgroups of order 2 in the product table for the permutation group of order 6, Table 1.6. Table 1.6 Permutation group of degree 3 E P2 P3 P4 P5 P6 E E P2 P3 P4 P5 P6 P2 P2 E P6 P5 P4 P3
Class each of the following permutations as even or odd. 1 1 2 4 1 4 (239) (2 319) (4 3 2 1) (a) 1 (b) (c)
In the permutation (536142) what number does 6 map to?
In the permutation (326415) what number does 5 map to?
Find a matrix representation for the "flip" of an equilateral triangle about its $a a$ axis. b a a b I
Consider the group $\Gamma=\{\mathbf{E}, \mathbf{A}, \mathbf{B}\}$ for the rotations of an equilateral triangle, Table 1.2. Are the following matrices a homomorphic representation of $\Gamma$
A diagonal matrix is a matrix that has zero elements except on its diagonal. Show that the product of two diagonal matrices is a diagonal matrix.
Find matrix representations for the 4-fold rotations of a square as described in Problem 8.Data from Problem 8A diagonal matrix is a matrix that has zero elements except on its diagonal. Show that
Which of the following matrices has an inverse? 1 0 3 0 ( -9) ( ) ( 22 ) (a) (b) -2 (c)
Consider the matrices $A$ and $B$.Find $A+B, A-B$, the product $A B$, and the product $B A$. 3 2 -31 A= -2 3 1 0 24 5 2 -3 B: B = 1 3 = -20 I 5
Consider the matrices $A$ and $B$.Find $A+B, A-B$, the product $A B$, and the product $B A$. A = B = = -1 5 4 -3 3 4 12 0 -31 2 -2 25 5 1 4 -3. 0 2/
Consider these two matrices and show that the determinant of their product is equal to the product of their determinants. This is a general result true for the product of any two square matrices. 2
For $n \times n$ matrices $A$ and $B$, show that $\widetilde{A B}=\tilde{B} \tilde{A}$.
For the matrix $A$, find $A^{*}, \tilde{A}$, and $A^{\dagger}$. 1 5 2 A = 3 0 14 -2 1
For the matrix AA, find A∗,~AA∗,A~, and A†A†. 1 3+i 2i A 3 0 -1+2i 14-3i -2 1-i
Consider the triangle rotation group $\{\mathbf{E}, \mathbf{A}, \mathbf{B}\}$. The group member $\mathbf{A}$ is a rotation by $120^{\circ}$. Show that $x, y$ are basis functions for
Consider the triangle rotation group $\{\mathbf{E}, \mathbf{A}, \mathbf{B}\}$. The group member $\mathbf{A}$ is a rotation by $120^{\circ}$. Show that $x^{2}-y^{2}, x y$ are basis functions
For the group of an equilateral triangle, let operation A be a "flip" - a rotation by $180^{\circ}$ about the $y$-axis. Show that $\phi_{1}=x^{2}+y^{2}$ and $\phi_{2}=z$ are basis functions
For the group of an equilateral triangle, let operation A be a "flip" a rotation by $180^{\circ}$ about the $y$-axis. Show that $\phi_{1}=x^{2}-y^{2}$ and $\phi_{2}=y z$ are basis functions
A 2-dimensional representation of a group member $\mathbf{T}$ is generated by the $\alpha$ set of basis functions to give \(D^{(\alpha)}(\mathbf{T})=\left(\begin{array}{cc}1 & 0 \\ 0 &
Under a similarity transformation with $\mathbf{S}$, group members $\mathbf{A}$ and $\mathbf{B}$ transform as $\mathbf{S A S}^{-1}=\mathbf{R}$ and $\mathbf{S B S}{ }^{-1}=\mathbf{T}$. Show
For the group $\{\mathbf{E}, \mathbf{T}\}$, the regular representation for $\mathbf{T}$ is $\left(\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}ight)$. A similarity transformation with a matrix
Consider the $2 \times 2$ matrix(a) Show that $\mathbf{S}$ is orthogonal.(b) Perform a similarity transformation with $\mathbf{S}$ on each of the following matrices:(c) Use the results from (b)
Consider the $2 \times 2$ matrix(a) Show that $\mathbf{T}$ is orthogonal.(b) Perform a similarity transformation with $\mathbf{T}$ on each of the following matrices:(c) Use the results from (b)
Find the character of each of the following matrices: 1 00 (+) (-1+i 0 3 0 1 0 0 2 2 4i 0 0 1 0 3+2i 1 0 0 0 1 (d) (e) 2 (-2) ( 3 -1 ) (a b) (A) (a) -3 (b) (c) 3
Here is the product table for the triangle rotation group $\{\mathbf{E}, \mathbf{A}, \mathbf{B}\}$. Write the matrices for the regular representation of group members $\mathbf{E}, \mathbf{A}$,
The noncyclic group of order 4 has members $\{\mathbf{E}, \mathbf{K}, \mathbf{L}, \mathbf{M}\}$, and its product table isWrite the regular representation of group member $\mathbf{K}$. E K L M E E
The cyclic group of order 4 has members $\left\{\mathbf{E}, \mathbf{A}, \mathbf{B}=\mathbf{A}^{2}, \mathbf{C}=\mathbf{A}^{3}ight\}$, and its product table is.Write the regular representation of
The $\mathbf{4 2 2}$ group describes the symmetries of a square, including "flips." It has eight members and five classes.(a) How many irreducible representations does the $\mathbf{4 2 2}$ group
The noncyclic group of order 4 has members $\{\mathbf{E}, \mathbf{K}, \mathbf{L}, \mathbf{M}\}$, with product table(a) What are the classes of this group?(b) How many irreducible representations
The cyclic group of order 4 has members $\left\{\mathbf{E}, \mathbf{A}, \mathbf{B}=\mathbf{A}^{2}, \mathbf{C}=\mathbf{A}^{3}ight\}$, and its product table is(a) What are the classes of this
Consider a group with general members $\mathbf{T}$. Starting from the relationwhere $h_{\alpha}$ is the dimension of the $\alpha$ irreducible representation and $n$ is the order of the
The three irreducible matrix representations of the $\mathbf{3 2}$ group are given. Demonstrate Theorem 5. Theorem 5 R n D(R) D (R)=8/8jj h
Here is the character table of the $\mathbf{3 2}$ group.Demonstrate Theorem 6 using this character table. {E} {A, B, C) {D, F} 1 1 1 1 A 1 1 1 2 20 -1
Here is the character table of the $\mathbf{3 2}$ group.Demonstrate Theorem 7 using this character table. {E} {A, B, C) {D.F} 1 1 A 1 -T 1 1 -1 1 2 0 -1
Consider the permutation group of 4 numbers (1234). There are two irreducible representations of dimension 1 , and the other irreducible representations all have dimensions greater than 1 . What are
The cyclic group $\{\mathbf{E}, \mathbf{A}, \mathbf{B}\}$ for the rotation of an equilateral triangle by $0^{\circ}, 120^{\circ}$, and $240^{\circ}$ has a matrix
Show that $(A \otimes B)\left(A^{\prime} \otimes B^{\prime}ight)=\left(A A^{\prime}ight) \otimes\left(B B^{\prime}ight)$. For simplicity let the matrices $A, A^{\prime}, B, B^{\prime}$ all be \(n
For the example of two masses and three springs use Eq. (3.5) to calculate the $c$ coefficients and show by direct calculation that $C B=\Omega C$. (Cnibijen) = (bij wijn; = 0. (3.5)
For the example of two masses and three springs let the springs be equal, k′=kk′=k. Use Eq. (3.5) to calculate the cc coefficients and show by direct calculation that CB=ΩCCB=ΩC. (cnibijen) =
Boron trifluoride, $\mathrm{BF}_{3}$, is a planar molecule, with the three fluorines bonded to a central boron. All three bond angles F-B-F are $120^{\circ}$.(a) What are its symmetry operations
Ammonia, $\mathrm{NH}_{3}$, is tetrahedral, with the three hydrogens in an equilateral triangle base plane and with the nitrogen at the top of the tetrahedron.(a) What are its symmetry operations
Here is the character table for point group 2 (Schönflies $\mathbf{C}_{2}$ ).Show by calculation that $x$ is a basis function for irreducible representation $B$. 1 22 A 1 1 B 1 -1
Here is the character table for point group $\mathbf{2 2 2}$ (Schönflies $\mathbf{D}_{2}$ ). There are three irreducible representations labeled $B$ because any of them can be a principal
Use the character table in Problem 6 to show by calculation that LzLz is a basis function for irreducible representation B1B1.Data from Problem 6Here is the character table for point group
Consider a planar system of three identical masses and three identical springs. At equilibrium each mass is at the apex of an equilateral triangle. A spring links each pair of masses.(a) How many
Consider a planar system of three identical masses and three identical springs. At equilibrium each mass is at the apex of an equilateral triangle. A spring links each pair of masses.Here is its
As in Problem 9, consider a planar system of three identical masses and three identical springs. At equilibrium each mass is at the apex of an equilateral triangle. A spring links each pair of
As in Problem 9, consider a planar system of three identical masses and three identical springs. At equilibrium each mass is at the apex of an equilateral triangle. A spring links each pair of
As in Problem 9, consider a planar system of three masses and three identical springs. At equilibrium each mass is at the apex of an equilateral triangle. A spring links each pair of masses.Two of
Xenon tetrafluoride, $\mathrm{XeF}_{4}$, is one the few noble gas compounds. Its molecule is planar, assumed to lie in the $x-y$ plane. Each F-Xe-F bond angle is $90^{\circ}$. Model the bonds
Consider the planar XeF4XeF4 molecule described in Problem 13. Assuming motion only in the x−yx−y plane, how many nontrivial normal modes are there?Data from Problem 13Xenon tetrafluoride,
The $\mathrm{NH}_{3}$ molecule is described in Problem 4. Here is its character table.Its nontrivial normal modes are basis functions for the irreducible representations $2 A_{1}+2 E$.(a) How
Boron trifluoride, BF3BF3, is a planar molecule with F−B−FF−B−F bond angles of 120∘120∘. It has the same symmetry operations as the mass and spring system in Problems 8 and 9, hence has
Which of the nontrivial normal modes of $\mathrm{H}_{2} \mathrm{O}$ is Raman active?
Copper is often the target in an $\mathrm{X}$ ray tube because of its high thermal conductiv ity. The target is typically mechanically rotated at several thousand revolutions per minute to average
Turquoise is an attractive bluish gemstone often fashioned into jewelry by Native Americans. In one XRD experiment, a turquoise sample was shown to have a triclinic Bravais lattice. In a Cartesian
The limestone White Cliffs of Dover, cave stalactites, and pearls are among naturally occurring forms of calcium carbonate $\left(\mathrm{CaCO}_{3}ight)$. Aragonite is one of the minerals found in
The primitive cell of a Bravais lattice is the smallest volume that can translate to fill its Bravais lattice completely. A primitive cell has only one lattice site (counting the sites shared with
There are often several choices for the basis vectors of a primitive cell (defined in Problem 4). Let aa be the length of one edge of a bec Bravais lattice.(a) One set of possible basis vectors for
Problem 2 lists experimentally determined basis vectors for a triclinic lattice. Calculate the basis vectors of its reciprocal lattice.Data from Problem 2Turquoise is an attractive bluish gemstone
Show that the translation group is cyclic by proving $\mathbf{T}_{2}=\mathbf{T}_{1}^{2}$.
Sketch a simple cubic lattice and shade a plane with Miller index (001).
Sketch a simple cubic lattice and shade a plane with Miller index (110).
From the XRD of aluminum powder Hull determined the lattice to be fcc, with lattice cell size $a=0.405 \mathrm{~nm}$ (modern value). He observed strong interference at Bragg angle
From the XRD of aluminum powder Hull determined the lattice to be fec, with lattice cell size $a=0.405 \mathrm{~nm}$ (modern value). He observed strong interference at Bragg angle
Avogadro's number $N_{A}$ is a universal constant equal to the number of particles (such as atoms, molecules) in one mole of a substance. One mole of aluminum has a mass of $26.98 \mathrm{~g}$.
The icosahedral group I (Schönflies) or 532 is large, with 60 members and five irreducible representations of orders $A=1, F_{1}=3, F_{2}=3, G=4$, and $H=5$. Table 4.6 shows its character table
The identity is the only symmetry operation for a triclinic lattice. Sketch its stereogram.
Sketch the diagram of symmetry elements for a square, including 4 fold rotations and flips.
Sketch the stereogram for a square, including 4-fold rotations and flips.
The figure is a stereogram for an orthorhombic lattice $(\alpha=\beta=\gamma=$ $90^{\circ}, a eq b eq c$ ). Including rotations and flips, what symmetry operations does the stereogram show?
The table gives the basis functions for the group 32. What are the gerade (+) and ungerade (-) irreducible representations of the group \(\overline{\mathbf{3}} \mathbf{m}=\mathbf{3 2} \otimes
The table gives the basis functions for the group $\mathbf{6 2 2}$. What are the gerade (+) and ungerade (-) irreducible representations of the group \(6 / \mathbf{m m m}=\mathbf{6 2 2} \otimes
Show that for a monatomic crystal $m=M$ the linear chain model predicts that the acoustic branch and the optical branch give the same value of $\omega$ at $q=q_{\max }$.
A sound wave is propagating along a linear diatomic chain $(M>n)$.(a) Calculate its maximum possible frequency.(b) What is the speed (phase velocity) of the sound wave traveling with its maximum
Beginning inventory: 100 units @$2.00 = $200.00During the month of January, the company sold 500 units.Compute the cost of goods sold and ending inventory. Purchases during the Month Jan. 15 Jan.
Company E buys 100 percent of Company F for $80,000. Accounts Other Assets Investment in Co. F Excess of Book Value over Investment Liabilities Common Stock Retained Earnings Company E Company F
Company C buys 100 percent of Company D for $130,000.a. Prepare journal entries to record the acquisition, assuming the Stanley Corporation ceases to exist as a separate corporate entity.b. Show the
Company A buys 100 percent of Company B for $55,000. Accounts Other Assets Investment in Co. B Liabilities Common Stock Retained Earnings Company A $ 90,000 55,000 $145,000 $
If the bond of the previous problem paid 10 percent interest per year ($100), at what price would it sell?Data from previous problem What is the present value of $1,000 due in ten years, discounted
Compute the payback for each of the cash flows in Problem 1. If the maximum acceptable payback period is four years, which (if any) of the cash flows would be accepted as a desirable investment?Data
In anticipation of increased steel prices, the Auto Company purchased a four months’ supply of steel. As of December 31, the costs of carrying this steel in inventory were $10,000,000 (the steel

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