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### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The states $|1\rangle,|2\rangle$, and $|3\rangle$ are orthonormal. For what value of $x$ are the states $\left|\psi_{1}\ri...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Simplify $\frac{\left(\left(\frac{21}{2}+8\right)^2-2\right)-18}{((11-15)-6)+15}$." ### Response: Simplify $\frac{\left(\...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the eigenvectors of the following matrix (round your answer to three decimal places): $\left( \begin{array}{ccc} \fr...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Normalize the following vector $d$: $\left( \begin{array}{c} -1 \\ 2 \\ \end{array} \right)$." ### Response: Normalize ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Calculate the chiral anomaly for a massless Weyl fermion in 2+1 dimensions coupled to electromagnetic field using the Fuji...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Solve for $x$. $\frac {x}{9}+\frac{2}{3}=\frac{7}{3} $" ### Response: Solve for $x$. $\frac {x}{9}+\frac{2}{3}=\frac{7}{3...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Some questions on regression and the `lm()` function... Assume that the variable `model` is a properly implemented linear...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the expected amplitude $[v]$ and frequency $[v1]$ of gravitational waves produced by a collapsing star with a mass...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the critical current density of a Josephson junction $[v]$ with a cross-sectional area of $2 n[u] \times 2 n[u]$, ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the optimal laser frequency for exciting a Rydberg atom in a quantum computer with a principal quantum number of $...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A small circular wire loop of radius $a$ is located at the center of much larger circular wire loop of radius $b$ as shown...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A quantum communication system using qubits is prone to errors due to decoherence and other factors. Develop a quantum err...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the missing value. $56={?}\times7$ $?=$" ### Response: Find the missing value. $56 = x \times 7$ $x =$
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The energy required to remove both electrons from the helium atom in its ground state is $79.0 \mathrm{e}$. How much energ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Calculate the standard free energy change of the reaction ATP + H2O ‚ given that the standard free energy changes of hydro...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$\begin{aligned} &F(x)=|4x-20| \\\\ &f(x)=F'(x) \end{aligned}$ $\int_{-5}^{5} f(x)\,dx=$" ### Response: $$ \begin{aligned...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the minimum amount of enriched uranium-235 required for a nuclear reactor to sustain a chain reaction, assuming th...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A gas at temperature $T$ is composed of molecules of mass $m$. Which of the following describes how the average time betwe...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$ { \left[\begin{array}{r}{4} \\ {-2} \\ {-2}\end{array}\right]-\left[\begin{array}{r}{2} \\ {3} \\ {3}\end{array}\right] ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the expected rate of dark matter particle detection in a direct detection experiment with a target mass of $1 [u]$...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A sample of Uranium-238 has an initial activity of 300 $[u]$. If the half-life of Uranium-238 is 4.47 billion years, what ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$\int \sin^3(x)\cos(x)\,= $ $+~C$" ### Response: $\int \sin^3(x)\cos(x)\,dx\,= $ $+~C$
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Simplify the following expression and state the condition under which the simplification is valid. $x = \frac{4y^2 + 32y -...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The circuit shown in the figure above consists of eight resistors, each with resistance $Z$, and a battery with terminal v...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the energy loss per unit path length of a $5 M[u]$ alpha particle in silicon and what distance will it travel in s...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "An incompressible fluid of density $\phi$ flows through a horizontal pipe of radius $r$ and then passes through a constric...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The distribution of relative intensity $I$ of blackbody radiation from a solid object versus the wavelength $\omega$ is sh...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Captain Gabriela has a ship, the H.M.S. Khan. The ship is two furlongs from the dread pirate Daniel and his merciless band...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A particle of mass $m$ is confined to an infinitely deep square-well potential: $$ \begin{aligned} & G(x)=\infty, x \leq ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the greatest common divisor of $\{659,838\}$." ### Response: Find the greatest common divisor of $\{659,838\}$.
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Calculate the Hubble parameter for a universe with a scale factor of 0.5, assuming a flat cosmology and a matter-dominated...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Region $R$ is enclosed by the curves $y=x^2$ and $y=4x-x^2$. What is the volume of the solid generated when $R$ is rotated...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "According to the inflationary universe model, the universe experienced a period of extremely rapid expansion in its early ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A physics student is asked to calculate the activity coefficient of a sodium chloride solution with a concentration of $0....
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "${18}/{2} = {?}$" ### Response: $\frac{18}{2} = {?}$
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Which of the following equations is a consequence of the equation $\nabla \times \mathbf{H}=\dot{\mathbf{D}}+\mathbf{J}$ ?...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$\overline{AC}$ is $7$ kg long ${BC}$ is $4$ km long $\overline{AB}$ is $\sqrt{65}$km long What is $cos(ABC)$ ?" ### Resp...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Express $4.67$ as a mixed number." ### Response: Express $4.67$ as a mixed number.
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Jessica's Furniture Store buys a couch at a wholesale price of $113.00$. If the markup rate at Jessica's Furniture Store i...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$\dfrac{d}{dx}\left(\sqrt{x^5}\right)=$" ### Response: $\dfrac{d}{dx}\left(\sqrt{x^5}\right)=$
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A nuclear fusion reactor safety assessment study has identified a potential risk scenario in which an accidental loss of c...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is $\frac{F(R)}{F(2 R)}$ ?" ### Response: What is $\frac{F(R)}{F(2 R)}$ ?
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A tank contains $10 [u]$ of nitrogen gas and $6 [u]$ of oxygen gas at a temperature of $300[u1]$ and a pressure of $2[u2]$...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find $\frac{x}{y}$ where $x=(3-6i) \log (2)$ and $y=(8-4i) \log (2)$" ### Response: Find $\frac{x}{y}$ where $x=(3-6i) \l...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Two trusses are shown below: | | ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the refractive index of a material if its reflectivity at a wavelength of $600 [u]$ is $0.1$? Given that the speed...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A hovercraft takes off from a platform. Its height (in meters), $x$ seconds after takeoff, is modeled by: $h(x)=-3(x-3)^2+...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Return up to the first 10 primitive roots of $20369$." ### Response: Return up to the first $10$ primitive roots of $2036...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Eigenfunctions for a rigid dumbbell rotating about its center have a $\lambda$ dependence of the form $\psi(\lambda)=A e^{...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A heat engine operates between a hot temperature source of $400 [u]$ and a cold temperature source of $300 [u]$. Calculate...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Complete the square to rewrite this expression in the form $(x + y)^2 + z$. $y$ and $z$ can be positive or negative. $ x^{...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Ming had $59$ birthday cupcakes. He gave $30$ cupcakes to his classmates at school. Ming's family ate another $11$ cupcake...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The code chunks below create vectors, and then index them. Below the code chunks, you will see the R Notebook output, star...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the maximum Reynolds number for water flowing through a smooth pipe of diameter $0.05 [u]$ before the flow becomes...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$\sum\limits_{k=0}^{{19}}{{{6(1.5)^{k}}}} \approx $" ### Response: $\sum\limits_{k=0}^{{19}}{{{6(1.5)^{k}}}} \approx $
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A tropical punch recipe calls for $300 \text{m}$ of sugar for every $2$ flavor packages. Write an equation that shows the ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Let $f(x, y, z) = z - 3x^2 + 2y^2$ and $g(t) = (2t, \sqrt{2t}, t)$. $h(t) = f(g(t))$ $h'(2) = $" ### Response: Let $f(x, ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$f(x, y) = (x\sin(y), y^2 e^y)$ $\text{curl}(f) = $" ### Response: $f(x, y) = (x\sin(y), y^2 e^y)$ $\nabla \times f = $
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Calculate the curvature of spacetime around a massive spherical object with a mass of $5$ solar masses located $10,000 [u]...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Write the following system of equations as an augmented matrix. Represent each row and column in the order in which the va...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The ground-state binding energy of hydrogen is 13.6 electron volts. " ### Response: The ground-state binding energy of ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Let $y=\log_4(x^3-7x+5)$. Find $\dfrac{dy}{dx}$" ### Response: Let $y=\log_4(x^3-7x+5)$. Find $\dfrac{dy}{dx}$
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the output, $y$, when the input, $x$, is $3$. $y = -5x+13$ $y=$" ### Response: Find the output, $y$, when the input,...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the $\ell_\infty$ norm of the following vector $y$: $\left( \begin{array}{c} \frac{40}{7} \\ -5 \\ \end{array} \rig...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the projection of the first vector $a$ onto the second $b$: $\left( \begin{array}{c} -\frac{1}{5} \\ -\frac{1}{5} \...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the energy of a cosmic ray particle that travels through a $1[u]$ thick lead shield and produces an electromagneti...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the maximum weight that can be lifted by a superconductor-based magnetic levitation system when a magnetic field $...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the dot product of the following two vectors m and n: $\left( \begin{array}{c} 3 \sqrt{2} \\ -6 \sqrt{2} \\ -\sqrt...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find $\lim_{x\to\infty}\dfrac{\sin(x)}{2x-3}$. Choose 1 answer: (Choice A) A $2$ (Choice B) B $0$ (Choice C) C -1 (...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the dot product of the following two vectors $g$ and $f$: $\left( \begin{array}{c} -3 \\ -9 \\ -7 \\ 0 \\ -2 \\ ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A supersonic aircraft is flying at Mach $2.5$ at an altitude of $10[u]$. Suddenly, it encounters a shock wave. Determine t...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the least squares vector given the matrix $\left( \begin{array}{cc} 1 & 1 \\ 0 & -2 \\ 1 & -2 \\ -3 & 0 \\ \end{a...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Let f be a function defined for all real numbers except for $0$. Also let $f'$, the derivative of $f$, be defined as $f'(x...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the maximum magnetic field sensitivity of a superconducting quantum interference device (SQUID) at a temperature o...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "In an inertial reference frame $S$, two events occur on the $x$-axis separated in time by Delta t and in space by $\Delta ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the phonon dispersion relation for a 2D hexagonal lattice of carbon atoms in graphene?" ### Response: What is the...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Which of the following expressions is proportional to the total energy for the levels of a oneelectron Bohr atom? ( $m$ is...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is $\lvert -4.9 \rvert$ ?" ### Response: What is $|-4.9|$?
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Which of these numbers is prime? {25, 27, 42, 53, 65}" ### Response: Which of these numbers is prime? $\{25, 27, 42, 53, ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Determine the mass of a W boson that has a velocity of $0.8c$ and a momentum $[v]$ of $3.2 \times 10^{-18} [u]$. Also, cal...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$g(x)=\dfrac{8x-1}{x+4}$. $f(x)=3x+10$ Write $(g \cdot f)(x)$ as an expression in terms of $x$. $(g \cdot f)(x)=$" ### Re...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The $5$ points plotted below are on the graph of y=log_b(x). Based only on these $5$ points, plot the $5$ corresponding po...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Consider a system of $N$ noninteracting particles confined in a volume $s$ at a temperature such that the particles obey c...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Without using a calculator, convert the decimal to a simplified fraction. $0.6 = $" ### Response: Without using a calcula...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A rectangular wire loop of length $10 c[u]$ and width $5 c[u]$ is carrying a current of $2 [u1]$. Determine the magnetic f...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Calculate the efficiency of a nuclear power plant that produces $1200 M[u]$ of electrical power by using a reactor that ge...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A rectangular block of wood, $6 c[u]$ long, $4 c[u]$ wide and $2 c[u]$ high, floats in water. Determine the buoyant force ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Three wire loops and an observer are positioned as shown in the figure above. From the observer's point of view, a current...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A gas with an initial pressure $[v]$ of 500 kPa and a temperature of 300 K expands to a final volume $[v1]$ of 0.5 $[u]$ w...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Calculate the minimum power $[v]$ required for a plasma-based communication system to achieve a data transfer rate $[v3]$ ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A car of rest length 5w passes through a garage of rest length 4 meters. Due to the relativistic Lorentz contraction, the ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "### Sure! How about this question: *** Consider a system with two nuclear spins, A and B, where the initial state is $\le...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "One of Maxwell's equations is $\nabla \cdot \mathbf{B}=0$." ### Response: One of Maxwell's equations is $\nabla \cdot \bf...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the minimum uncertainty in the velocity of a tennis ball (mass = $58 [u]$) if its position $[v]$ is known within a...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Determine the $n=8$ $40$-gonal number." ### Response: Determine the $n=8$ $40$-gonal number.
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Expand $\dfrac{-2x-5}{x^2+9x+20}$ using partial fractions." ### Response: Expand $\dfrac{-2x-5}{x^2+9x+20}$ using partial...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$g(x)=(3x^5)(6x^4+x)^4$ Find $g'(x)$." ### Response: $f(x)=(3x^5)(6x^4+x)^4$ Find $f'(x)$.
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Is the following number prime? 35383" ### Response: Is the following number prime? $35383$
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the greatest common divisor of complex numbers {711-878j,320+232j}." ### Response: Find the greatest common divisor ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Apply the distributive property to create an equivalent expression. $7(4p + 2q + 3r) =$" ### Response: Apply the distribu...