0 stringlengths 229 2.91k |
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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... |
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