0 stringlengths 292 2.43k |
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### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Suppose that a system in quantum state $i$ has energy $E_{i}$. In thermal eq... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"An organ pipe, closed at one end and open at the other, is designed to have ... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
""A gas occupies a volume of 0.5 $[u]$ at a pressure of 2 $[u1]$ and a temper... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"In Biophysics, consider the case of a lipid bilayer subjected to mechanical ... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Rewrite the function by completing the square. $f(x)= x^{2} -9 x +14$ $f(x)=... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Solve for $x$: $7x + 9 = 2x + 3$
"
### Response:
Solve for $x$: $7x + 9 = 2... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"What is the predicted gamma-ray signal from a 100 $[u]$ WIMP dark matter par... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"According to the inflationary universe model, the universe experienced a per... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Find one value of $x$ that is a solution to the equation: $(x^2-6)^2=-3x^2+1... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Evaluate the function $f(g)=\cos \left(6 x+\frac{13}{2}\right) \tan \left(6 ... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Ming had $59$ birthday cupcakes. He gave $30$ cupcakes to his classmates at ... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Mr. Bray prepares a list of $43$ US presidents, $8$ of whom died in office. ... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"$a_n=\frac{(-5)^n}{(n+3)8^{n+1}}$
1) Find $\lim_{n\to\infty}\left| \frac{a... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A particle moves along the x -axis. The function $x(z)$ gives the particle's... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A square has an area of $49$ square meters. What is the perimeter of the squ... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Find the plane defined by the following points:
${\left\{\frac{1}{2},3,-\fra... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"You may find it helpful to read through the **Supplement** at the end of *Ha... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Without using a calculator, convert the decimal to a simplified fraction. $0... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"The quantity $\alpha$ in the photoelectric equation is the minimum energy re... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Using the principles of magnetic resonance and NMR spectroscopy, calculate t... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Consider the quasi-static adiabatic expansion of an ideal gas from an initia... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Let $f(x)=\begin{cases} (x-2)^2&\text{for }x \leq 2 \\ 2-x^2&\text{for }x>2 ... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Convert the following matrix to reduced row echelon form:
  
$$
... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A particle is initially at rest at the top of a curved frictionless track. T... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"$\frac{6}{3} = {?}$"
### Response:
$\frac{6}{3} = {?}$
<|end_of_text|>
|
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Alice and Bob want to communicate securely using quantum cryptography. Alice... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Two sinusoidal waveforms of the same frequency are displayed on an oscillosc... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A box contains 10 red balls, 3 green balls, and 3 blue balls. If a ball is r... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A fluid flows through a pipe of radius $[v]$ with a laminar flow. The fluid ... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"$f(x)=\frac{1}{1+6x}$ Find a power series for $f$."
### Response:
$f(x)=\fr... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"What is the force required to stretch a single strand of DNA to $1.5$ times ... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"In January, the average temperature z hours after midnight in Mumbai, India,... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"What is the probability of a neutrino produced as an electron neutrino chang... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A physics student is required to determine the gravitational redshift experi... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Evaluate the definite integral. $\int^{1}_{9}\left(-15\sqrt{x}\right)\,dx = ... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A semiconductor material with a conductivity $[v]$ of $5 \times 10^{-3} [u]$... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"The capacitor in the circuit above is charged. If switch $S$ is closed at ti... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A particle accelerator is producing gamma rays with a frequency of $4.5 \tim... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A laser beam with a wavelength $[v]$ of $500 n[u]$ is diffracted through a s... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A spaceship is orbiting a planet that has a surface gravity field $[v]$ of $... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"[embedded]
You are building a toy car to race in a miniature version of... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A polygon with $6$ vertices has the coordinates
$$
\left(
\begin{array}{cc}... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Determine the $n=8$ $40$-gonal number."
### Response:
Determine the $n=8$ $... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"The distribution of relative intensity $I$ of blackbody radiation from a sol... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"What is the critical temperature of the high-temperature superconductor YBa2... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Multiply
$\left( \begin{array}{ccc} 1 & 2 & 0 \\ -2 & 2 & -2 \\ -2 & -1 &... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"What is the entanglement entropy of a 1-dimensional quantum field theory sys... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"The Gades Foundation and HBM Corporation are eager to donate generously to t... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Solve for $x$ and $y$ using elimination. ${-4x-y = -16}$ ${-3x+y = -5}$"
##... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"$ {-6 ~ \left[ \begin{array}{cc} 0 & -1 \\ -2 & 0 \\ 3 & -2 \end{array} \rig... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A pair of electric charges of equal magnitude $q$ and opposite sign are sepa... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Much of our analysis work involves data cleaning and preparation.
You may f... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"The *diagram* below illustrates the operation of a **4-bit** optical encoder... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"What is the critical temperature of a superconducting material made up of le... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"An alternating current electrical generator has a fixed internal impedance $... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Photons of wavelength $\theta$ scatter elastically on free protons initially... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"At the fair, I collected $15$ balloons. Some of them blew away, and I had $1... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"What is the thickness of the boundary layer that forms on a flat plate subme... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A car with a cross-sectional area $[v]$ of $2.0 [u]$ is traveling at a speed... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"The energy eigenstates for a particle of mass $g$ in a box of length $z$ hav... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A forest has 800 pine trees, but a disease is introduced that kills 1/4 of t... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"$f(x)=(3x^5)(6x^4+x)^4$ Find $f'(x)$."
### Response:
$f(x)=(3x^5)(6x^4+x)^4... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A particle with mass $[v]$ and velocity $[v1]$ collides elastically with ano... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"The energy required to remove both electrons from the helium atom in its gro... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"What is the maximum amount of information that can be transmitted through an... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"**What are fits and tolerances?**
* Up until last week, all dimensions th... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Determine the average number of gluons exchanged in a high-energy collision ... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Determine the probability of a Higgs boson decay into a bottom quark-antiqua... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A cube has a constant electric potential $P$ on its surface.
"
### Respons... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Add. $64.43 + 12.8=$"
### Response:
Add. $64.43 + 12.8=$
<|end_of_text|>
|
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A rectangular loop of wire carrying a current of 2 A is placed perpendicular... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Statement:
A spaceship travels at a speed of $0.6c$ relative to the Earth. A... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"What is the Schwarzschild radius for a black hole with a mass $[v]$ of 1 mil... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"What is the thermal conductivity of a silicon semiconductor at a temperature... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Find the cross product of the following vectors $a$ and $g$:
$\left( \begin{... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"The geometric sequence $(a_i)$ is defined by the formula: $a_1 = -\frac{5}{2... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Return up to the first 10 primitive roots of $20369$."
### Response:
Return... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Omar did 89 push-ups at night. Brandon did 26 push-ups in the morning. How m... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"What is the angle of deflection $[v]$ of light as it passes near a massive o... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Subtract the second matrix from the first:
$\left( \begin{array}{cc} -7 & -6... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Using the Van der Waals equation of state, determine the Boyle temperature o... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Calculate the beta function for a specific quantum field theory model, namel... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"All of the 4th grade teachers and students from Santa Rita went on a field t... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Find the eigenvalues of the following matrix:
  
$$
\left(
\begi... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A cylindrical tube of mass $M$ can slide on a horizontal wire. Two identical... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"What is the energy required to flip a qubit in a superconducting circuit wit... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"A $\pi^{0}$ meson (rest-mass energy $135 \mathrm{A}$ ) is moving with veloci... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"### Introduction:
In ME1 Materials, you have learned about tensile (brittle... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Solve the equation: $x + 25 = 26$ $x=$"
### Response:
Solve the equation: $... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"What is the thermal conductivity of a silicon nanowire with a diameter $[v]$... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"$f(x,y) = \sin^2(x) - \cos(y)$ What is $\frac{\partial f}{\partial y}$"
###... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Two observers $O$ and $O^{\prime}$ observe two events, $A$ and $B$. The obse... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"What is vector a + vector b"
### Response:
What is vector $\bf{a} + vector ... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Solve for $y=f(x)$ given the following parametric equations:
  
... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Find the eigenvectors of the following matrix:
$$
\left(
\begin{array}{cc}
... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"### Ace:
A spaceship travelling at a velocity of $0.8c$ relative to Earth re... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Let $f(x)=\sqrt{2x-4}$ and let $c$ be the number that satisfies the Mean Val... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Multiply. $8 \times 24.05 =~$
  
[embedded]"
### Response:
Mult... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"Consider 1 mole of a real gas that obeys the van der Waals equation of state... |
### Instruction:
Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations.
### Statement:
"What is the bandgap energy of a (7,7) single-walled carbon nanotube? Use the... |
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