I've heard conflicting answers, and would like to see the record set straight:  An jet/propeller airplane is traveling on a giant treadmill at takeoff speed. Will the plane takeoff, or will it remain on the runway, and why?
So this has puzzled me for many a year... I still am no closer to coming to a conclusion, after many arguments that is. I don't think it can, others 100% think it will.   If you have a plane trying to take off whilst on a tread mill which will run at the same speed as whatever the planes tires rotation speed is will it take off?  [edited to be more clear]  The question is simple. Will a plane take off if you put this plane onto a treadmill that will match whatever speed the plane wheels are moving at. So the plane should not be able to move.  This is a hypothetical situation of course. But I am very interested.
Cancelling a Schengen Visa via the Italian Consulate How to backup an Android device? Is this intended behavior (with plain XeTeX):  \input tikz \tikz\draw[dashed] node {$3T\over4$}; \bye   It renders as: !?  The fraction line is dashed, too! Is this intentional? Is there something I can do to change that? I know I can separate the fraction into its own node, but other than that? How to assign a SSL Certificate to IIS7 Site from Command Prompt Can you advise me whether it is possible or not to assign a SSL Certificate to a website in IIS7 using the APPCMD application?  I am familiar with the command to set the HTTPS Binding  appcmd set site /site.name:"A Site" /+bindings.[protocol='https',bindingInformation='*:443:www.mysite.com']   and how to obtain current mappings   %windir%\system32\inetsrv\Appcmd   but can not seem to find any way to map a site to a certificate (say the certificates hash for example) I quite enjoy paying attention to how I design my documents and presentations. I usually spend hours thinking over and designing my slides for a workshop or presentation, so that they are aesthetically pleasing and as intuitive as possible. Likewise I recently started revising my CV I figured and I wanted to make it stand out a bit more. (Just to make it clear I don't mean making a clown of a document but just better use of colors, contrast and design elements.)  I have long wondered whether or not this is something that can backfire, since most documents in academic context are extremely plain, at least in my experience. It's very common to see the default Powerpoint slides (white bg, black arial text) or .   My question is as follows: is putting time and effort into design of academic documents something that can backfire? Will I risk being prejudged with first impressions such as "well he put much effort in the presentation his documents, perhaps because the content is sub-par"?     I realize that the question might be somewhat subjective from person to person but I encourage everyone to consider it in terms of this SE blog entry: . Kernel of a substitution map Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$ No more updates for Google Chrome 32-bit I am using Google Chrome 48.0 32-bit. Today when I launched Google Chrome, I got this message:    This computer will soon stop receiving Google Chrome updates because this Linux system will no longer be supported   I thought Ubuntu 14.04 is supported for five years, what's exactly happening here?  And on 64-bit Ubuntu, I get an error from Update Manager and apt-get update:  Failed to fetch http://dl.google.com/linux/chrome/deb/dists/stable/Release  Unable to find expected entry 'main/binary-i386/Packages' in Release file (Wrong sources.list entry or malformed file)   Some index files failed to download.   They have been ignored, or old ones used instead. What license does Ubuntu fall into (GPL, MIT, a mix)? Would it be legal to modify it and redistribute my modified version? Why are Bitmap-Fonts used automatically? Changing units of measurement in a simple regression model Since I updated the system to 10.11.5, the Facebook message notification is not showing message text.   Is this a bug in this software upgrade of OSX? 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. How to make a window always stay on top in .Net? Schengen Visa four years- 90 days stay I have been granted multiple entry Schengen Visa valid for 4 years with the duration of stay of 90 days. Does it mean only 90 days of stay in total during a 4 years period?  I'll be travelling to Schengen Area in September for 25 days, then after 2 month or so I will travel again for 30 days. Similarly, I'll be traveling to the Schengen Area in the future depending on the business meetings.  How will I know, that how many days are left? On what basis the calculations are done?  Also, please explain the "90/180" rule. How do I color intersection of two ellipses in different color. For instances, the ellipses should themselves be colored as yellow and their intersection as red. My code for drawing ellipses is given below  \draw (-4,0) ellipse (8 and 3); \draw (8,0) ellipse (8 and 3);   UPDATE: In the comments to individual answers, I have requested to show it for three ellipses. Should we restrict signup for a service to Facebook accounts only? How does a graduate program's admissions committee operate? How does a typical graduate program's admissions committee operate? (In the US --- I understand that in Europe admissions are often structured differently.)  My mental model at the moment is several professors sitting in a conference room with a stack of printed applications and a few piles: accept, maybe, and reject. Three or so professors will read an application and then make a decision. If the volume of applications is large enough, multiple meetings might be required. This is purely my imagination --- I don't know how accurate this model is.  Of course, I'm sure that how admissions are handled depends greatly on the school, program, and department. I'm interested in a few data points to get a rough idea of what the average is.  A few more specific related questions:   How much time does a typical committee spend on each application? I suspect there's a distribution. Obviously unqualified applicants will probably have their applications tossed into the reject pile pretty quickly. Qualified applicants' applications might receive more attention. Do admissions committees look online for more information about an applicant? I've read some professors (in CS --- not my field) will look at a student's research/project website, but I have no idea how common this is. Upper bound on $\chi(G)$ for a triangle-free graph I'm struggling with the following question;     For every graph $G$ such that $K_3 \not\subseteq G$ (i.e. $G$ does not contain a triangle), prove that $\chi(G) \leq 2\sqrt{n} +1$ (where $\chi(G)$ denotes the chromatic number).   Any hints? I really cannot see the connection between the triangle-free nature of $G$ and a chromatic number being bounded above by $O(\sqrt{n})$. Does the PS-Vita support PSP games Is the PS-Vita backwards compatible with PSP games?  Some games I would like to play include Final Fantasy 7: Crisis core, Jak and Daxter: The Lost Frontier, Coded Arms, Tekken: Dark Resurrection, and Secret Agent Clank.