What is Unit: Definition and 1000 Discussions

UNIT is a fictional military organisation from the British science fiction television series Doctor Who and its spin-off series Torchwood and The Sarah Jane Adventures. Operating under the auspices of the United Nations and initially led by Brigadier Lethbridge-Stewart, its purpose is to investigate and combat paranormal and extraterrestrial threats to Earth. Several UNIT personnel (such as the Brigadier, Sergeant Benton and Mike Yates) played a major role in the original Doctor Who series, and it was a regular feature from The Invasion (1968) until The Seeds of Doom (1976).
Originally referred to as the United Nations Intelligence Taskforce, executive producer Russell T Davies said in 2005 that the UN was no longer happy to be associated with the fictional organisation and the UN's full name could now no longer be used. However, the "UNIT" and "UN" abbreviations could be used as long as it was not explained what the letters stood for. In 2008, he announced that the organisation's name had been changed to the Unified Intelligence Taskforce. This new name was first mentioned on-screen in "The Sontaran Stratagem", also in 2008, in which it was indicated in a line of dialogue that the United Nations still supports UNIT with funding.

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  1. A

    All Eigenvalues Lie on the Unit Circle

    Hi everyone Consider a 2x2 partitioned matrix as follow: A = [ B1 B2 ; B3 B4 ] I'm sure that all eigenvalues of A are on the unit circle (i.e., abs (all eig) = 1 ). but, I don't know how to prove it. Is there any theorem?
  2. K

    Visualizing Unit Vectors: A Step-by-Step Guide

    How to explain unit vector visually?
  3. F

    Unit (cm) any alternative to the obvious?

    The problem involves a spray drying process in which a liquid containing dissolved or suspended solids is sprayed into a chamber that has air flowing into it which contains water. One outlet stream has the wet air, and the other has dry solids. The Air inlet stream is described as having...
  4. G

    Unit Cell - Linear Density - BCC & FCC

    Unit Cell -- Linear Density -- BCC&FCC Homework Statement Calculate the linear density for the most densely packed directions in BCC and FCC. Note the difference in linear density. Note the difference in linear density. Homework Equations LD = #of atoms/length The Attempt at a...
  5. R

    The difference between structural unit and repeating unit?

    Homework Statement The difference between structural unit and repeating unit Homework Equations The Attempt at a Solution http://en.wikipedia.org/wiki/Structural_unit wikipedia gives an example with polyethylene terephthalate but I can't figure it out based on the slight...
  6. M

    Unit vector in direction of max increase of f(x,y,z)

    Homework Statement Find the unit vector e at P=(0,0,1) pointing in the direction along which f(x,y,z)=xz+e-x2+y increases most rapidly. The Attempt at a Solution In order to find the direction where f increases most rapidly, I found the second derivative of f. I don't know how to put the...
  7. L

    How to Convert Units for Finding the Mass of a Star?

    Homework Statement Need help with some unit conversion. The problem asks to find mass of a star. p=1.58e9 seconds a=7.61" d=8.15e18 cm +-.001 Homework Equations M=(4pie^2 d^3 a^3)/Gp^2 The Attempt at a Solution My problem is with " arcsecond i think it is. The mass should be...
  8. T

    Determining the Uncertainty of a Unit Vector using Error Propagation

    Homework Statement Consider the points (x, y) = (0,0) and (100,10). Calculate the unit vector u pointing from the first to second. If each coordinate has an uncertainty of +/-2, calculate the uncertainty in u using propagation of error, but making reasonable approximations based on the values...
  9. A

    Area of the region inside the unit circle

    Homework Statement The area in the region inside the unit circle and above the graph of f(x) = x^5 Homework Equations I don't know how to type the equation in here but the area is the integral between two integration points of the higher curve minus the lower curve. The Attempt at a...
  10. I

    Solving Unit Vectors Problem: Calculate Forces at B

    OK here's the problem. I am completely unsure how to solve it my teacher never even did an example like this before. The total force exerted on the top of the mast B by the sailboat's forestay AB and backstay BC is 180i- 820j (N). What are the magnitudes of the forces exerted at B by the...
  11. I

    Unit Vector Question. *updated*

    OK here's the problem. I am completely unsure how to solve it my teacher never even did an example like this before. The total force exerted on the top of the mast B by the sailboat's forestay AB and backstay BC is 180i- 820j (N). What are the magnitudes of the forces exerted at B by the...
  12. E

    Unit circle and tangent line

    Homework Statement We are given the unit circle and the point (5,2). There are two lines that are tangent to the unit circle and they both intersect at the point (5,2). What are the points where these lines are tangent with the unit circle. Homework Equations Tangent line of a circle at...
  13. I

    Question About Forces Using Unit Vectors

    OK here's the problem. I am completely unsure how to solve it my teacher never even did an example like this before. The total force exerted on the top of the mast B by the sailboat's forestay AB and backstay BC is 180i- 820j (N). What are the magnitudes of the forces exerted at B by the...
  14. I

    Question about Forces Using Unit Vectors

    The question is: The total force exerted on the top of the mast B by the sail boats forestay AB and backstay BC is 180i-820j (N). What are the magnitudes of the forces exerted at B by the cables AB and AC? I need some serious help with this question. Any help.
  15. M

    Unit cell dimensions of crystal structure

    Hello all, I already have the answer to my question, but what I would like to know is why. My question is: why in the question below is the plane 111 used to find ao and not another plane? An ordered compound of NiAl has a cubic structure with one formula unit/cell. One Al atom at...
  16. E

    How can I use inversion in a circle to simplify a problem?

    Can somebody give me an example whereby I use the inversion with respect to a circle (unit circle or otherwise) and the problem becomes easier. I guess I am asking: how do I make use of this notion. Or a problem that involves inversion, period. Thank you
  17. O

    Can the Dot Product of Two Unit Vectors Ever Be Less Than 1?

    I need certain stopping criterion for approximating one unit vector with another. In case there is a perfect match (after a number of iterations), the dot product of the vectors is 1. I need to know (and have a reasoning for) whether in any other case the dot product of the original unit vector...
  18. R

    Show that the given function maps the open unit disk into the upper half plane

    Homework Statement 4. Let w = f(z) = i(\frac{1-z}{1+z}). Show that f maps the open unit disk {z \in C | z < 1} into the upper half-plane {w\in C|Im(w) >0}, and maps the unit circle {z\in C||z|=1} to the real line. Homework Equations I was given this hint: "set w=i(\frac{1-z}{1+z}) and...
  19. A

    How to change unit of quantum to energy

    the quantum unit of LUE is umolco2m-2s-1 how can i change it to energy unit ,like gC/MJ i have been puzzle for many days Can somebody help me
  20. B

    Calculating the mass per unit length of a string based on the graph of f vs. 1/L

    Homework Statement The frequency of a vibrating string is set to 15, 20, 25, 30, or 35 Hz and the length needed to attain a standing wave (mode 1) is recorded. A graph of frequency versus 1/L is recorded. Calculate the mass per unit length of the string. The resulting graph has the...
  21. V

    Help with a vector proof about perpedndicular unit vectors

    Prove that if a(t) is a unit vector whose components are functions of t, then the vector b(t) = da(t)/dt is perpendicular to a(t) here i have the parameters that make a(t) a unit vector: 1 = f(t)^2 + g(t)^2 i know of the example sinxi + cosxj = a(t) but that is the only one i can get to work. I...
  22. E

    Which unit of pressure is used in the ideal gas law?

    The ideal gas law states that pressure (P) is equal to the product of density (N), the ideal gas constant (R) and temperature (T): P = N x R x T I can't figure out which unit the pressure is actually in, although it does seems to work out as the figure I'm supposed to get with a 11706.85°...
  23. P

    Assistance on building energy unit with alternators

    If someone could assist me with some information re: the following it would be very much appreciated. I am planning to build an energy system for my home to address the drastically increasing power bills we have been getting as a result of the unusually hot weather lately. Problem is I am not...
  24. T

    Astrophysics - tricky unit conversions?

    Homework Statement I've got a radius of 22.69kpc, and a velocity of 180km/s. I wish to find the angular rotation speed in units of arcsec/year. I'm stuck at the moment The Attempt at a Solution Starting with the basic v=r\omega, I transpose to get \omega=v/r. For now, I'm going...
  25. X

    Unit Conversion: What went wrong?

    Homework Statement Pressures up to 3000 atm are measured with a dead-weight gauge. The piston diameter is 0.17 (in). What is the approximate mass in (lbm) of the weights required? The Attempt at a Solution Abs. pressure = Gauge pressure + Atmospheric pressure = 3000 atm + 1...
  26. A

    Unit Step Function: u(-t) Meaning & Negative Time

    what does the u(-t) mean in unit step funtion in basic function of signal and system?how can be time taken as -ve?
  27. A

    Work done in moving a unit positive charge in space by an external force

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  28. O

    Finding Self-Intersection and Unit Tangent Vectors of γ(t)

    Homework Statement Show that the curve γ(t)=(t²-t+1,t³-t) has exactly one self-intersection point and finnd the two unit tangent vectors (in the direction of increasing t) at this point. I have found the self intersection. I know that a unit tangent vector is the derivative of each...
  29. phy_optics

    Converting Lux to Watts: A Quick Guide

    Hello frnds! Can anybody convert the following factors? V/(lx-s) to V/(um/cm2) at 555nm ?? Thank you.
  30. D

    Magnetic field strength - unit conversions

    I have to spec a sensor to monitor the magnetic field of a DC solenoid element. The specification for the solenoid includes its length, DC resistance, current at the applied supply voltage, and most importantly, the expected Dipole Moment of the unit, as 42 Am^2. I plan to attach a solid...
  31. jegues

    Tangent unit vector of a curve

    Homework Statement See first figure. Homework Equations The Attempt at a Solution See second figure. When I set t = 0 in \vec{r(t)} I get 0\hat{i} +2\hat{j} + 1\hat{k}. I know this is a vector and not a point but it has the same "coordinates" as the point they are asking us...
  32. K

    Instantaneous Unit Conversion between CGS and SI units

    In doing some research, I cam across an equation for instantaneous radiated power, with the CGS units "erg/(sec rad cm)", rad being radians (not rad the unit for radiation exposure). Try as I might, I'm not able to come up with a way to convert it to the SI units for watts. Does anyone know...
  33. G

    Formula for Normal Unit Vector on Ellipse at (x,y)

    Given the formula for an ellipse in x and y and centered on the origin, I need a formula for the x and y components of the normal unit vector at any point (x,y) on the ellipse (y>0). My calculus skills are rusty, and I haven't been able to figure this out. Thanks in advance for any help.
  34. M

    Which of these have higher output per square unit*, phototransistors,

    Which of these have higher output per square unit*, phototransistors, photodiodes or APD photodiodes.?
  35. Y

    Help with Poisson problem in a unit ball.

    I cannot get the answer of the problem as in the book but the book usually right. I did it in 2 totally different ways and I still get my own answer. Can anyone help me double check? This is to find u(r,\theta,\phi) given: \nabla^2 u(r,\theta,\phi) = -k u(r,\theta,\phi) = f(r)=1 \hbox {...
  36. AJ Bentley

    What is the Unit of Momentum?

    I was just trying to get my head around a point that was a little obscure, when I realized that part of the problem was that in thinking of momentum I hadn't got a name to hang on the unit. Unlike energy, where you just think so-many-Joules or Force (ditto-Newtons), you get stuck with this...
  37. Q

    Definition of unit of electric current

    The ampere is that constant current which , if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 × 10 ^{–7} Newton per...
  38. L

    Question regarding maximum on a unit disc

    Homework Statement Find the maximum of |ez| on the closed unit disc. Homework Equations |ez| is the modulus of ez z belongs to complex plane Maximum Madulus Theorem - Let G be a bounded open set in complex plane and suppose f is a continuous function on G closure which is analytic in...
  39. majormuss

    Do I have memorize the entire Unit circle ?

    Do I have memorize the entire Unit circle ?? Homework Statement I am currently takin a trig class and I was a bit daunted by the Unit Circle and all its special angles. My question is... Do I haveto memorize the entire Unit Circle and its angles?? Will it be given to me during exams(as...
  40. T

    Vectors- gradient and normal unit vector- is this correct?

    Homework Statement For the scalar field f(x, y, z) = x2 − y2 − z find gradf and normal unit vector to a surface f(x, y, z) = 0 at the point (1, 1, 0). Homework Equations The Attempt at a Solution I calculated gradf= 2xi -2yj -k at (1,1,0) this is = 2i -2y -k normal unit...
  41. L

    Compute Unit Normal Vector: Why Derivative is Orthogonal

    The unit normal vector N of a given curve is equal to the first derivative with respect to t of the unit tangent vector T'(t)divided by the norm of T'(t) (For a parametric vector equation of parameter t.) I realize this works because T(t) is orthogonal to T'(t), but I don't understand why the...
  42. V

    How Accurate Is the Pressure Calculation for Argon in a Cubic Container?

    Can I please check if I've converted these units right? I'm doing a question and got the answer a few order of magnitudes out. Question: Argon has a collision cross section of 0.36nm^2. At what pressure is the mean free path of argon atoms equal to the length of the side of a 1cm^3 cubic...
  43. J

    Calculating Hypervolume/Hypersurface of Unit Ball in n Dimensions

    How do you derive the hypervolume/hypersurface of the unit ball in n dimensions? I thought it'd be trivial but oh well. I'm guessing switch to n-D spherical coordinates? Is there an argument which doesn't involve explicitly calculating too many things? :x
  44. T

    How to find the unit vector in cylindrical coordinates

    So I'm trying to find out what the procedure is to convert a cartesian unit vector to a cylindrical unit vector. Any thoughts?
  45. J

    Calculating Ionic Radius of Chloride Ion in LiCl (NaCl Structure)

    Q.The unit cube length of LiCl (NaCl structure) is 5.14 amstrong . Assuming anion-anion contact, calculate the ionic radius for chloride ion. How to assume anion-anion contact ? Can anyone help with a 3D figure?
  46. C

    Average Radius of a Unit Cell: Na

    What is the average radius for a unit cell, for example, for Na? Is it the average of the ionic radii for the different coordination numbers (weighting each coordination number the same)? Or would it be the covalent radii or something else?
  47. K

    Solving Equations Using the Unit Circle

    Homework Statement Find all solutions to the equation below such that -180° \leq x \leq 90° 2sin2x + sinx = 0Homework Equations The Attempt at a Solution 2sin2x + sinx = 0 sinx[2sinx + 1] = 0 sin x = 0 sinx= -1/2 x = {0° + 360°n {-180° + 360°n n\epsilonI
  48. B

    Differential Geometry: Unit Normal Field

    Let M be the surface defined by z=x2+3xy-5y2. Find a unit normal vector field U defined on a neighborhood of p on M. First, I reparameterized the equation for the surface to get x(u,v)=(u,v,u2+3xy-5y2). Next I found two tangent vectors xu(u,v)=(1,0,2u+3v) and xv=(0,1,3u-10v). The next step is...
  49. K

    Finding the Unit Normal to a Plane

    Homework Statement Find the unit normal to the plane 3x + 5y - z = 2. What is the distance of the plane from the origin. Homework Equations The Attempt at a Solution The normal vector in component form --> (3, 5, -1) Magnitude of the normal vector --> √35. Divide the normal vector by its...
  50. 1

    Unit conversion litres to gallons or vice versa

    Homework Statement One bottle of magnum contains a volume of 1.5litres. 1 bottle of boream contains a volume of 0.792 us gallons. How many bottles of magnum will fit in 1 bottle of boream? Homework Equations litres to galons galons to litres The Attempt at a Solution Uh...i've...
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