studiot

It can be a little confusing and rather depends what you mean by 'vector'. Tensors are uniquely defined and can generally be written as matrices (though not all matrices represent tensors). As such they contain row and column 'vectors'. Tensors do not, however, have 'components' in the vector sense, that represent one quantity (the vector magnitude) that can be resolved in separate directions. Tensors have 'elements', that may not all be of the same type. These elements correspond to the elements or entries of the matrix. So for instance the stress tensor has 3 axial stress and 6 shear stress elements. These cannot be lumped (like forces which are vectors) into a single magnitude and resolved into particular directions. So in this sense tensors are more complicated objects than vectors. Scalars are the simplest, they offer one piece of information only eg the mass. Vectors are next and offer two pieces of information eg magnitude and direction. In this sense tensors are the generalisation that extends the idea to n pieces of information. On this scheme we would refer to the order of the tensor as (n-1) So a scalar is a tensor of zero order A vector is a tensor of first order and the first tensor we would recognise as such would be a second order tensor, such as the stress tensor, that contains 9 pieces of information. Set against this is the subject of linear algebra which defines Vector Spaces and the members or elements of such spaces as 'vectors' if they obey the axioms of linear algebra. Tensors obey these linear axioms so can themselves be classed as vectors in this wider sense. There are various algebras or rules for combining scalars, vectors and tensors. Does this help?

Such devices exist (using radar) but are hardly at school science level. There are also radio regulatory issues. Are you just programming a simulator or are you thinking of building hardware and what do your teachers think? A slightly less ambitious project where all the other vehicles carry 'bleepers or flashers' could be made to work, within the ambit of school science. This could well show all the principles involved, without the need to try to produce specially modified radar.

That's a bit narrow don't you think? What about ancient France and St Francis of Assis? or talking of France what about the relationship in philanthropy between ancient Rome and modern France http://www.theguardian.com/culture-network/culture-professionals-blog/2012/jul/24/arts-philanthropy-france-le-mecenat

Doesn't that just apply to this thread?

Unfortunately I have been away for a couple of weeks and have just come across this one. However we can work through it if you are still interested, there is much insight to be gained from this one. I will call the third vertex of the triangle C. Well I agreed with your calculations in parts (1) 110J and (2) 375K , and I agree that if you calculate the change in internal energy from A to B and subtract the work (with due regard to sign) you will obtain the heat change but I calculated the work from A to B to be 190J, not 220J as you have it. Edit I would guess that you have added the area between the BC and the pressure axis (110J) to the triangle. This is of course the leg where no work is done since the volume change is zero. You should be calculating the area between AC and the Volume axis (80J), which will add to get you the proper answer. You correctly calculated the change in internal energy to be 45J so (45 - 190)J = -145J, the heat change required. You have correctly identified Cv as being 3R/2, but did not specifically note that this is because helium is a monatomic gas (you need to use all the facts given in the problem). This makes Cp = 5R/2 since we are using ideal gas laws as the equations of state. Why do you think it was important for the questions to state that the change AB was made slowly? When we have constant volume conditions we use Q = CvdT; This can therefore be done for the leg CA of the cycle. When we have constant pressure conditions we use Q = CpdT; This can therefore be done for the leg BC of the cycle. However in general when the conditions are neither constant volume nor constant pressure we cannot directly use the specific heats but must use the equations for internal energy or enthalpy. http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/shegas.html

Perhaps the most worrying aspect of the thread title is the ISDS section of the proposed TTIP trade deal that allows corporations (that don't pay any tax) to sue a country for loss of income as well. http://en.wikipedia.org/wiki/Transatlantic_Trade_and_Investment_Partnership

I would like to add the note that the '3-sphere' ajb refers to is the hypersurface, not the hypersolid. quote from wiki : http://en.wikipedia.org/wiki/3-manifold

Is this a (small) rock sample or a full outcrop? If the latter, do you have stratigraphic information about the rocks the granite has intruded into? It will be younger than any of these.

You should also look up slatey cleavage in the second case.

Yes

Most people find a diagram helpful which is why one has bee suggested. If you wish to struggle on without one then let us work through your problem using the alternative method imatfaal offered Starting at the first part What do you think the statement Q intersection R means in words? Never mind the negation or complementation in the other questions for the moment they are only a distraction to the first part.

So how about your diagram as suggested?

I suggest you draw a diagram shown the regions for each set involved. What do you notice?

Having read a greater % of the wlad's other thread first I skipped out this one just as you were posting Well put sir+1 To wlad I suggest that instead of posting two lengths of toilet roll, you post a much shorter piece establishing a few facts we can agree on and then go from there.

No. pzkpfw has already told you the simple answer. A question of the sort you posed is meant to be answered using only the information given. If a piece or pieces of information are missing so any solution is impossible, the question is at fault. A word of advice. In the past students could expect to need to use every piece of information to solve all the question. So if you had a piece of information 'left over' unused then you could be sure you have made a mistake and missed something. I have seen some modern questions that contain unecessary information as a deliberate distraction.

A good idea would be to post your thoughts on what how to approach this question, rather than just post the question. There is no need to convert to centigrade, the calculation can be done perfectly satisfactorily in fahrenheit. Give us a clue what you already know.

fiveworlds Do I take it you have no further interest in this subject, but can't be bothered to tell me?

I didn't ask for your views on it just if you have ever seen it for yourself? Surely this is a simple question that does not warrant a link to 5 page pdf? Am I wasting my time trying to engage you in friendly discussion or did my last post#27 merit no other comment?

It is also the slope of the X-Y trajectory at t=0, that is it is [math]{\left. {\frac{{dy}}{{dx}}} \right|_{t = 0}}[/math] The point I wanted to establish was that this slope changes throughout the trajectory. function was there anything else you wish to discuss about this subject? You can derive further information from your formula if you wish.

It would help if you got your Latex errors mended. However is angle theta not the initial angle of projection? So are you expecting this to remain constant throughout the trajectory?

I'm sorry, I'm not following this. How and why is the semiconductor connected to the outer electrode? What do you think this will achieve, since connecting the semiconductor at one point says nothing about the potential anywhere else in the semiconductor? What do you mean by saying that the electrolyte is earthed? Again this has implications for the potential distribution and therefore the capacitance. This is getting very complicated and a numerical mode as opposed to an analytical one, may be the only way forward. There is capacitance between any two points in space that have a potential difference between them, governed by the intervening material. You have asked about a coax cable, but show saline between the inner and out. Please explain. Finally please confirm this is not the beginning of some HHO or other crank generator device discussion.

Yes you are quite right. Silly me. How did you come to a product of differential coefficients?

What I am really saying is you need to give more detail of the situations you wish to compare. One important variable is the 'Characteristic Dimension'. What are these for the situations in air an water? Once you have settled this that will fix some of your other parameters/boundaries.

I was trying to discern a question in that first post. The main difference between air and water is that air is compressible in a big way. The other big difference is that water can flow in open channels and often has a free surface. Gases 'expand to fill theor container'. Obviously air is also less dense, and has lower viscosity so any formulae that depend upon these properties will also change., that of course is partly taken care of in dimensionless number modelling, but it doesn't always work. So where do you want to enter the arena?

The derivatives will only be partials in more than one (spatial) dimension. The equation, as written, is linear and also conservative. I confess I am not a fan of string theory but the small vibrations requirement is to ensure the linearity and therefore the conservation. So small means small enough for the restoring force to be linear. If a non linear equation is used it will be dissipative at best or dispersive at worst, neither of which model observed reality that the strings (or whatever) endure and do not fade away. What other equation would you suggest?