Active transformation and passive transformation of a scalar field
Active versus passive transformations
Why doesn't Mac OS X source ~/.bashrc? How can there be animals on the surface in Zion's world? It is apparently canon that  in Neo's day.  However, in the first movie, The Matrix, Morpheus tells Neo that one of the things known for certain is that humans "burned the sky" in order to deny solar engery to the machines, which in turn led to the humans who survived the War being plugged into the Matrix to provide bioelectric energy to supply the machines.  If there's not enough sunlight for solar power, how can there be enough to grow plants to serve as food for animals?  Low levels I can understand -- house plants, at least, thrive in conditions too dim for solar panels to produce cost-effective power -- but every surface scene we see in the trilogy is as dark as a cloudy night; light coming only from the machines.  That wouldn't begin to support photosynthesis, which means all animal life would starve in, at most, a matter of a few years. Show that, if $a$ and $h$ are positive numbers, $h &lt; a^2$, then $$\sqrt{a^2 + h}-a &lt; \frac{h}{2a} &lt; a - \sqrt{a^2 - h}$$  I've been working on this problem for about 2 hours now, but I've made no progress. I'm not looking for an answer, but I just need some help to get me started since we didn't practice inequalities this complex in highschool. Thanks.   All I can tell is that we're supposed to take the square root of an expression at some point since one inequality ( h &lt; a^2 ) becomes two.   Edit : Thank you guys for the replies, but I'd appreciate only hints in the future (like Robert Israel) so that I can learn. Regardless, I found a different way to do it, so it's cool :) No room for a new \dimen Amy: What day is it today?    Tom: It's Monday. Hmm... I like Monday.   Amy: What do you have today?   Tom: We have math, science and art.What about you?   Amy: We have English and P.E. What do you have tomorrow?    Tom: We have art and P.E.tomorrow.    Amy: Oh, great.      I can understand that "What about you" means "What do you have today?"  But I wonder whether "What about you" is an elliptical sentence. If it is, what is the full sentence? If it isn't, how to parse this structure? You "show" someone a picture. You "---" someone a song? In , we have a verb meaning &quot;to show&quot; corresponding to &quot;to see/to look&quot;, and we have a different verb corresponding to &quot;to hear/to listen&quot;:  inti tara stampa (you look at a picture.) ---- jiena nurilek stampa (I show you a picture) inti tisma' diska (you listen to a song.) ----- jiena nsemmagħlek diska (I 'show' you a song)  In English, do you &quot;show someone a song&quot; (sounds weird to me) or is there a verb that corresponds more directly to the Maltese insemmgħek? Are any fictional worlds available in some GIS format? Is there any fictional world (e.g. ,  etc.) which could be used in a GIS context?  For example, an MBTiles archive and a shapefile or any other format usable with OpenLayers / Polymaps / Leaflet? I've seen references to curried functions in several articles and blogs but I can't find a good explanation (or at least one that makes sense!) Not able to understand the meaning of question? car moving with a speed of 40 km / h can be stopped by applying brakes after at least 2 m. If the same car is moving with a speed of 80 km / h, what is the minimum stopping distance  Does this mean that after 2 m, You will apply brakes and then it stops. What is the retardation value  with which you are brakes.I am not understand the meaning of the values. How do you return to the default view (the one you see when blender starts)? Resolve $\lim_{x \to 0} \frac {\tan 3x}{\tan 5x}$ I started resolving this limit:  $$\lim_{x \to 0} \dfrac{\tan 3x}{\tan 5x}$$  so:  $$\begin{align}\lim_{x \to 0} \dfrac{\tan 3x}{ \tan 5x} &amp; = \lim_{x \to 0} \dfrac{\frac{\sin 3x}{\cos 3x }}{\frac{\sin 5x}{\cos 5x}} \\ \\ &amp; = \lim_{x \to 0} \dfrac{ \sin (3x) \cdot \cos (5x)}{ \sin(5x) \cdot \cos (3x)}\\ \\ &amp; = \quad?\end{align}$$  Could someone help me please I want to create a standalone python script using QGIS python API (PYQGIS) for education. First I create a model and export that model to python script.  original python script from the export :  ##=name ##raster=raster ##stat=output html outputs_QGISRASTERLAYERSTATISTICS_1=processing.runalg('qgis:rasterlayerstatistics', raster,stat)   Next I read this  and I tried to follow this tutorial to create my script.  Final script :  import sys from qgis.core import QgsApplication from PyQt4.QtGui import QApplication app = QApplication([]) QgsApplication.setPrefixPath("/usr", True) QgsApplication.initQgis()  # Prepare processing framework  sys.path.append('/home/username/.qgis2/python') from processing.core.Processing import Processing dem='aster.tif' slope='slope.tif' aspect='aspect.tif' outputs_SAGASLOPEASPECTCURVATURE_1=processing.runalg('saga:slopeaspectcurvature', dem,6,1,1,slope,aspect,None,None,None,None,None,None,None,None,None,None) Processing.initialize()  # Exit applications QgsApplication.exitQgis() QApplication.exit()   If I run this script it works fine without error but I don't take some export like aspect and slope (these can't be found?). Any idea why I can't take exports ?  I use Ubuntu and python 2.7 and QGIS 2.18.1.    i try to this script :  import sys from qgis.core import QgsApplication sys.path.append('/usr/share/qgis/python/plugins') import processing a=processing.alglist() print a processing.alghelp("saga:slopeaspectcurvature")   and i take that print any idea why ?  Algorithm not found   but if i use this module in QGIS work fine. How to run updmap-sys after installing cm-super? My original question was:   The answer that seems suitable to my cause is to install cm-super. I did that (using package manager [winxp 32 bit, MikTex installation 2.9 recently updated]). But still the command  \usepackage{cm-super}    yields an error.  User H Cavendish suggested to run updmap-sys, but I am not sure about how to do that on WinXP.   2011 November 04 edit: I made it sure that I have installed 'cm-super' - but still get the same error:   I have also tried updating the file name databases - but no avail. How to differ sessions in browser-tabs? Input image strip without stretching to fit output frame When you add an image strip to the Video Sequence Editor, it stretches/shrinks your image to fit the full output frame.  How can I add an image at its original resolution?  For example, if I add a 60x60 pixel image, it should appear very small in the final 1080p render. Anchor Text code string is automatically modified by WordPress I have created an ad for a merchant wanting to rent ad space on my website home page. After creating the ad, (anchor text and pic/graphics with embedded hyperlink) the merchant has requested I remove my url from the ad code. The anchor text along with the embedded hyperlinks links to the merchant's home page.  Problem is I don't know how my url was added to the code as I never inputted it in the original code in the first place. Somehow it was added by I think, WordPress or my server (PHP).  When I view the page source I do see my url was added to the ad code.  Can anyone help explain this and tell me how I can remove the url? Also, if I am able later to remove my url, how will it affect the hyperlink and anchor text?  Thank you, -Dan  Hi s_ha_dum,  I have read your answer and have now made sure the code reads as abosolute url.  Here it is with absolute url:  &lt;strong&gt;If you are interested in helping others treat and prevent hypertension, consider a healthcare degree from &lt;a href="http://elearning.loyno.edu/"&gt;Loyola Online Courses today!&lt;/a&gt;&lt;/strong&gt;   It still shows in page source however with my url addended to the code string.  What am I not understanding? Thank you! I'm suppose to prove the following...  Let $A$ be a nonempty subset of $\mathbb{R}$. If $\alpha = \sup A $ is finite show that for each $ \epsilon &gt; 0 $ there is an $a \in A $ such that $\alpha - \epsilon &lt; a\leq \alpha $.  This is what I have so far...  Proof: We claim that $\alpha = \sup A $   Then by definition of a supremum $\alpha $ is the least upper bound of set A  Thus $\forall a \in A$,  $a \leq \alpha$   Suppose $\epsilon &gt; 0$   Then $\alpha - \epsilon &lt; \alpha $.   Thus $\alpha - \epsilon &lt; a\leq \alpha$.   I feel like I'm missing some step between my last and second to last step so what am I forgetting? Also is the rest of my proof right? How do I use one shape to delete a portion of another shape? I have created an arrow shape (rightmost in image), from which I wish to cut out the majority so that only two thin sides remain. The most accurate way to do this would be to duplicate the shape and to somehow use the duplicate (leftmost in image) to remove the chunk that I no longer desire from the original. I am not sure what to do after the duplication, however, or if this method is even possible? Is there a better one? Over the years I have slowly developed a  that validates MOST email addresses correctly, assuming they don't use an IP address as the server part.  I use it in several PHP programs, and it works most of the time.  However, from time to time I get contacted by someone that is having trouble with a site that uses it, and I end up having to make some adjustment (most recently I realized that I wasn't allowing 4-character TLDs).  What is the best regular expression you have or have seen for validating emails?  I've seen several solutions that use functions that use several shorter expressions, but I'd rather have one long complex expression in a simple function instead of several short expression in a more complex function. Proving a sequence defined by a recurrence relation converges How can I prove that this iterative sequence converges to $2$? Can I use the convergence definition?  $$a_{n+1} = \frac{a_n}{2} + \frac{2}{a_n},\qquad  a_0 = 4  $$  Thanks for the help.