Examples of using Mathbf in English and their translations into Indonesian
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Ecclesiastic
And of a tensor A{\displaystyle\mathbf{A}}.
S{\displaystyle\mathbf{s}} is the quantized spin vector.
Given our distribution function,there is a maxima corresponding to R= 0{\displaystyle\mathbf{R} =0}.
For a given b{\displaystyle\mathbf{} b}, heavier objects fall more quickly.
The vector area is a combination of the magnitude of the area through which the mass passes through, A, and a unitvector normal to the area, n^{\displaystyle\mathbf{\hat{n.
An object's average acceleration over a period of time is its change in velocity(Δ v){\displaystyle(\Delta\mathbf{v})} divided by the duration of the period( Δ t){\displaystyle\Delta t.
Since each electron has a magnetic moment in a magnetic field, it will be subject to atorque which tends to make the vector L{\displaystyle\mathbf{L}}.
This vector can beexpressed as a function of the particle position X{\displaystyle\mathbf{X}} in some reference configuration, for example the configuration at the initial time, so that.
The acoustic wave equation(and the mass and momentum balance equations) are often expressed in terms ofa scalar potential φ{\displaystyle\varphi} where u∇ φ{\displaystyle\mathbf{u}=\nabla\varphi.
Thus, F m d v d t m a,{\displaystyle\mathbf{F}=m\,{\frac{\mathrm{d}\mathbf{v}}{\mathrm{d} t}}=m\mathbf{a},} where F is the net force applied, m is the mass of the body, and a is the body's acceleration.
This system can be rearranged into a matrix equation of the form Ax=b,{\displaystyle A\mathbf{x} =\mathbf{b},} whose solution is x=A- 1b.
Mathematically, a¯ Δ v Δ t.{\displaystyle{\bar{\mathbf{a}}}={\frac{\Delta\mathbf{v}}{\Delta t}}.} Instantaneous acceleration, meanwhile, is the limit of the average acceleration over an infinitesimal interval of time.
The velocity, or the rate of change of position with time, is defined as the derivative of the position with respect to time: v d r d t{\displaystyle\mathbf{v}={\mathrm{d}\mathbf{r}\over\mathrm{d} t}\,\!
Volumetric flow rate can also be defined by: Q v⋅ A{\displaystyle Q=\mathbf{v}\cdot\mathbf{A}} where: v flow velocity A cross-sectional vector area/surface The above equation is only true for flat.
Assuming harmonicity of the scattering centers in the material under study, the Boltzmann distribution implies that q⋅ u{\displaystyle\mathbf{q}\cdot\mathbf{u}} is normally distributed with zero mean.
W∫ C F⋅ d s{\displaystyle W=\int_{C}\mathbf{F}\cdot\mathrm{d}\mathbf{s}} This says that the work( W{\displaystyle W}) is equal to the line integral of the force F along a path C; for details see the mechanical work article.
The wave function is a function of the two electron's positions: ψ ψ( r 1,r 2).{\displaystyle\psi=\psi(\mathbf{r}_{1},\mathbf{r}_{2}).} There is no closed form solution for this equation.
Using$\ mathbf{ a}=-\ omega^ 2/\mathbf{r}$ the speed required to obtain a modest 1/6 of Earth gravity in order to provide a small but meaningful experience of"laying down" rather than floating is $\omega=1.3\text{s}^{-1}$ which works out to one revolution every 5 seconds, or a rotation frequency of 0.2 Hz.
Since each electron has a magnetic moment in a magnetic field, it will be subject to atorque which tends to make the vector L{\displaystyle\mathbf{L}} parallel to the field, a phenomenon known as Larmor precession.
Two similar notations are used for the Euclidean norm of a vector x:‖ x‖,{\displaystyle\left\|\mathbf{x}\right\|,}| x|.{\displaystyle\left|\mathbf{x}\right|.} A disadvantage of the second notation is that it is also used to denote the absolute value of scalars and the determinants of matrices and therefore can be ambiguous.
With m being an object's rest mass, v and v its velocity and speed, and c the speed of light in vacuum, we use the expression for linear momentum p m γ v{\displaystyle\mathbf{p}=m\gamma\mathbf{v}}, where γ 1/ 1- v 2/ c 2{\displaystyle\gamma =1/{\sqrt{ 1-v^{ 2}/ c^{ 2.
The differential form of Fourier's law of thermal conduction shows that the local heat flux density,q{\displaystyle\mathbf{q}}, is equal to the product of thermal conductivity, k{\displaystyle k}, and the negative local temperature gradient,-∇ T{\displaystyle-\nabla T.
Recall that according to the principle of equally likely a priori probabilities, the number of microstates, Ω, at some physical value is directly proportional to the probability distribution at that physical value, viz; Ω( R) c P( R){\displaystyle\Omega\left(\mathbf{R}\right)=cP\left(\mathbf{R}\right)} where c is an arbitrary proportionality constant.
Due to the convolution theorem, the integral becomes a simple product, P( ω) ε 0 χ e( ω) E( ω).{\displaystyle\mathbf{P}(\omega)=\varepsilon_{0}\chi_{e}(\omega)\mathbf{E}(\omega).} Note the simple frequency dependence of the susceptibility, or equivalently the permittivity.
The correct equation of motion for a body whose mass m varies with time by either ejecting or accreting mass is obtained by applying the second law to the entire, constant-mass system consisting of the body and its ejected/accreted mass; the result is F+ u d m d t m d v d t{\displaystyle\mathbf{F}+\mathbf{u}{\frac{\mathrm{d} m}{\mathrm{d} t}}=m{\mathrm{d}\mathbf{v}\over\mathrm{d} t}} where u is the velocity of the escaping or incoming mass relative to the body.
We also write the Schrödinger equation of a single non-relativistic particle under the influence of a potential V(r,t),{\displaystyle V(\mathbf{r},t),} one very famous example of the Schrödinger equation as it pertains to physical systems.
By considering a freely jointed, non-interacting polymer chain, the end-to-end vector is R∑i 1 N r i{\displaystyle\mathbf{R}=\sum_{i=1}^{N}\mathbf{r}_{i}} where ri is the vector position of the i-th link in the chain.
More generally, the torque on a point particle(which has the position r in some reference frame) can be defined as the cross product: τ r× F,{\displaystyle{\boldsymbol{\tau}}=\mathbf{r}\times\mathbf{F},} where r is the particle's position vector relative to the fulcrum, and F is the force acting on the particle.
In the Bohr model, the allowed orbits were derived from quantized(discrete) values of orbital angular momentum, L according tothe equation L n⋅ ℏ n⋅ h 2 π{\displaystyle\mathbf{L}=n\cdot\hbar=n\cdot{h\over 2\pi}} where n 1, 2, 3,… and is called the principal quantum number, and h is Planck's constant.
Then one defines a closed line segment as above, and an open line segment as a subset L that can be parametrized as L{ u+ t v∣ t∈( 0, 1)}{\displaystyle L=\{\mathbf{u}+t\mathbf{v}\mid t\in(0,1)\}} for some vectors u, v∈ V{\displaystyle\mathbf{u},\mathbf{v}\in V\,\!