While doing an English test I've found this question :     A ___________ lives in that house.         fat, small man   small, man fat   man, fat small   small, fat man        Could someone give me an explanation of what's the right answer, and more importantly why?  Is there a difference between British and American English in this case?
I remember being taught that the correct order of adjectives in English was something along the lines of "Opinion-Size-Age-Color-Material-Purpose."  However, it's been a long time and I'm pretty sure I've forgotten a few categories (I think there were eight or nine). Can anyone fill them in?
Let $R$ be a ring (unital, not necessarily commutative), $M$ a finitely presented left $R$ module. Suppose $m_1,\ldots,m_n\in M$ generate $M$. This determines a surjection $f:R^n\to M$.     Must the kernel of $f$ be finitely generated?   This is true by definition if the generating set $m_1,\ldots,m_n$ is the one coming from the finite presentation of $M$. Can't quantum teleportation be superluminal some percentage of times? I apologize if this is a really silly question.   In the (textbook) quantum teleportation algorithm, in the step right after Alice has measured her system but before she has sent her classical information to Bob, she is about to send one of the following values: 00,01,10,11.   What if Bob doesn't want to wait and simply takes a guess? Wouldn't there then be superluminal communication 25% of the time? This System Information is from Process Explorer. There is still physical memory available but the system shows nearly no RAM left.  Task Manager also shows that about 74% of total RAM is used.  Since installing Windows 8.1, the computer had 4+8=12 GB of RAM. I upgraded it by changing the 4 GB to an 8 GB module. Could that be the problem? Or is this behavior normal and I've just misunderstood the meaning of available physical memory? Reprojecting LiDAR data with libLAS, error: "latitude or longitude exceeded limits"? Does the (relativistic) mass change? Why? I learned recently that when an object moves with a velocity comparable to the velocity of light the (relativistic) mass changes. How does this alteration take place? Sum and product of Martingale processes Given two Martingale processes $(X_t)$ and $(Y_t)$, are their sum $(X_t+Y_t)$ and their product $(X_t \times Y_t)$ also Martingale?  If not, will the two $(X_t)$ and $(Y_t)$ being independent grant their sum and product Martingale? Thanks! Comparing $\pi^e$ and $e^\pi$ without calculating them How can I  compare (without calculator or similar device) the values of $\pi^e$ and $e^\pi$ ? Integral $\int_0^1\sqrt{1-x^4}dx$ I am asked to show $\int_0^1\sqrt{1-x^4}dx=\frac{\{\Gamma(1/4)\}^2}{6\sqrt{2\pi}}$. I know the gamma function is defined by $\Gamma(n)=\int_0^\infty x^{n-1}e^{-x}dx$. I tried to substituted $x^2=\sin(t)$ but couldn't go further. I am really questioned how a radical function can convert to an exponential one? :-0 Thank you. Given the function   $$ f(x) = \left\{\begin{array}{cc} e^{- \frac{1}{x^2}} &amp; x \neq 0 \\ 0 &amp; x = 0 \end{array}\right. $$  show that $\forall_{n\in \Bbb N} f^{(n)}(0) = 0$.  So I have to show that nth derivative is always equal to zero $0$. Now I guess that it is about finding some dependencies between the previous and next differential but I have yet to notice one. Could you be so kind to help me with that?  Thanks in advance! Are PS+ free games region-locked? I have a PSN account that belongs to region X. It has a PS+ subscription. I have acquired many games throughout the years; some are PS+ free games, some are digital medias bought from PS Store. I'm moving to region Y.   Question: will I be able to play all of them normally on while I'm in region Y, specially those free PS+?  In other words, will I be able to keep using the same PSN and PS+ accounts and get access to my games in the library?  PS: I believe it is not possible to change country of a PSN account, isn't that so? When you energise a taut string, the following resonant modes of vibration occur:    Plotting on the frequency domain, you can see their corresponding frequencies:    But what is the underlying physical principle? Why does this happen?  Is there any way of explaining it that could be understood by a smart 15 year old?  EDIT: I'm going to give my best attempt so far. Here goes:   We can start with sympathetic resonance. Sounding a particular frequency, a pure sinewave.  And noticing the string resonates sympathetically at the frequency of each harmonic. Say this is explained and understood. Now imagine that plucking a string is equivalent to a burst of white noise, which contains frequencies all the way through the spectrum. This could be approached backwards, by starting with random frequencies and noticing that resultant wave produced looks like white noise.   If the above is scientifically correct, then it restricts the domain of the question.  I would really like to be able to understand it scientifically and also be able to explain it intuitively.  PS Images from Google Maps Location History is showing an incorrect location I have a major problem that I hope someone can help with. On my Google Maps feature under my Location History it shows a location that I was never at at any point, but when my wife happened to see that location she doesn't believe me that the GPS could be wrong and pinpoint that location if I was never there.  I was first wondering myself how could that could be possible if I was never there or my phone was never at that location that was 35 miles away from me and second is there any way I could prove the GPS being wrong? Can I contact Google Maps and can they give an official printout of that certain day and every location I was? I really need to prove my honesty to her and hope there is a way. Is Duck/Duct tape safe to use to insulate mains wires? Question says it all really. Based in the UK so mains is 240v and 20 amps. It's a lighting circuit. How to delete empty folder with thumbs.db without disabling thumbnails I often have problem to delete a folder that contains a thumbs.db file. Also tools like  fail. It seems to be loccked by os for some unknown reason. The only solution i found in the net was to disabling thumbnails in windows but this is a bad workaround isn't it?  Is there a "normal"(or official, supported by MS) way to delete an empty folder that only contains a thumbs.db? I have an email account that has passed 60GB of emails, and currently I'm having a lot of trouble using an email client to archive emails of last year (2011).  Via terminal, I am trying to use  to locate the files between 2011-01-01 and 2011-12-31, but no avail.  How can I find files between two dates?  If relevant, the end goal will be a batch that will move each file found, matching the date interval, to a folder. How to show a binomial random variable dominates another binomial random variable with a smaller success value? Let $X\sim B(n,p_h)$ and $Y\sim B(n,p_\ell)$ be two random variables following a respective binomial distribution, where $p_h&gt;p_\ell$. I want to show that  $$P(X\ge\alpha)\ge P(Y\ge\alpha),$$ for any $\alpha\in\{0,1,\dots,n\}$. In other words, I want to show  $$P(X\ge\alpha)=\sum_{i=\alpha}^{n}\binom{n}{i}p_h^i(1-p_h)^{n-i}\ge P(Y\ge\alpha)=\sum_{i=\alpha}^{n}\binom{n}{i}p_\ell^i(1-p_\ell)^{n-i}.$$  The statement to be proven is obviously true, but proving it is extremely difficult (at least for me). Can anyone give me some guidance on proving it?  It would be nice if someone can give an algebraic proof too, that is, show that  $$\sum_{i=\alpha}^{n}\binom{n}{i}p_h^i(1-p_h)^{n-i}\ge \sum_{i=\alpha}^{n}\binom{n}{i}p_\ell^i(1-p_\ell)^{n-i}.$$  Thank you very much! What's the difference between a Long Term Support Release and a Normal Release? What are the differences between an Ubuntu Long Term Support release (LTS) and a normal release? I have been texture painting in look dev mode. But when i try to render it, everything looks very dark. I have 3 sun lights in my scene, ambient turned on in Eevee settings. What am i missing? I really like the look of my scene in Look Dev mode, how can i achieve the same look when my scene is rendered too? Prove inequality $\sqrt{\frac{2a}{b+a}} + \sqrt{\frac{2b}{c+b}} + \sqrt{\frac{2c}{a+c}} \leq 3$ Why is the mol a fundamental physical quantity? I am starting to study physics in detail and as I read about physical quantities, I was puzzled why mol (amount of substance) is taken as a physical quantity.  A physical quantity is any quantity which we can measure and has a unit associated with it. But a mol represents the amount of substance by telling the number of particles (atoms, molecules, ions, etc.) present. So it is a pure number and numbers are dimensionless. So mol should not be considered a physical quantity.  Also, fundamental physical quantities should be independent of each other. I am wondering whether mass and mol are independent. This is so as they surely affect each other as we can evidently see while calculating the number of moles and using the mass of that sample for calculation.  So how is the mol a fundamental physical quantity and independent of mass?