The law of the conservation of energy describes that energy cannot be created nor destroyed however in fact only changes form.   How does this law explain the energy transferred by magnetic fields?
When a permanent magnet attracts some object, lets say a steel ball, energy is converted into for instance kinetic energy and heat when attraction happens, and they eventually collide. Does this imply that energy is drawn from the magnetic field and the magnet is depleted, making it weaker and weaker for each magnetic attraction performed?  (if the answer requires Quantum Mechanical explanations, please elaborate :))
The company I work for has asked me to attend a training class on the other side of the country.  However my situation is my drivers license expired a few days ago. I do however have a separate printed email stating that the license has been renewed.  This drivers license is my only ID that shows both my name &amp; photo.  Is it possible to be able to board a flight with the expired drivers license and the printed email showing that it was renewed? Feature Request: Could 7.5K users have the privilege of proposing synonyms without the 5 upvotes per tag requirement?  (in other words unrestricted synonym suggestion)  Background: I would like to be able to suggest tag synonym suggestions.  I do not however, have the required , but someday I will.  Yet many 2.5K users do not have the requisite 5 upvotes in each tag in order to propose synonyms.  I realize that this  for low-rep users.  But could it be made available to users with 7,500 rep?  At this level, they've clearly demonstrated an understanding of the Stack Exchange site.  Note: I'm not requesting the ability to create synonyms -- merely synonym suggestions.  I believe this privilege is currently only available to moderators? (and  )  Lastly, please note that  clearly demonstrates the breadth of simple synonym suggestions which could be made (almost every Stack Exchange site has some), but many haven't even been suggested yet. Endow $S^3$ with its standard smooth structures from the stereographic projections, i.e. $$\chi_1:S^3 \setminus \{(0,0,0,1) \} \to \mathbb{R}^3, \chi(x,y,z,t) = \frac{1}{1-t}(x,y,z) $$ and $$\chi_2: S^3 \setminus \{(0,0,0,-1) \}   \to \mathbb{R}^3, \chi_2(x,y,z,t) = \frac{1}{1+t}(x,y,z).$$   Do the same for $S^2$, call the charts $\eta_1, \eta_2$ (in the same order as the ones for $S^3$). Now, consider the complex projective space $\mathbb{C} \mathbb{P}^1$ endowed with the smooth structure given by the charts $\{(U_0, \varphi_0), (U_1, \varphi_1)\},$ $$U_0 = \{[z_0:z_1] \ \mid \ z_0 \neq 0 \} \text{ and } U_1 = \{[z_0: z_1] \ \mid \ z_1 \neq 0 \},$$ where $[x:y]$ represents the complex line through the point $(x,y)$ and $0$ in $\mathbb{C}^2$, and $$\varphi_0([z_0: z_1]) = \frac{z_1}{z_0} \text{ and } \varphi_1([z_0: z_1]) = \frac{z_0}{z_1}. $$   Now define the Hopf maps: $$h: S^3 \to S^2, h(x,y,z,t) = (x^2+y^2-z^2-t^2, 2(yz-xt), 2(xz+yt)) $$ and $$H:S^3 \to \mathbb{C} \mathbb{P}^1, H(x,y,z,t) = [(x+iy):(z+it)]. $$  Is there an easier way to prove that $h$ is a well-defined smooth submersion and that $H$ is a smooth submersion (with respect to the respective smooth structures)? By this I mean we can of course compute $\eta_i \circ h \circ \chi_j^{-1}, \forall i,j \in \{1,2 \}$ and $\varphi_k \circ H \circ \chi_l^{-1}, \forall k,l \in \{1,2 \}$ and prove that they are smooth (in the classical real-analysis sense) and that they are submersions, but this is a very tedious process. So, are there easier ways to do this? Will this maybe be easier if we switch the smooth structure of the unit spheres from stereographic projections to, say, normal projections (though we increase the number of combinations of charts to verify from 4 to 48), since they induce the same smooth structure? How can I discover any USB storage devices and/or CD/DVD writers available at a given time (using C# .Net2.0).  I would like to present users with a choice of devices onto which a file can be stored for physically removal - i.e. not the hard drive. Why the default eth0 interface is down by default on CentOS? When my receiver that I have hooked up to my pc turns on it causes my monitors to turn black is there a way to stop this? $2\times2$ matrix $A$ such that $A$ has one independent eigenvector while $A^{2}$ has two independent eigenvectors How to add some non-standard font to a website? Is there a way to add some custom font on a website without using images,  or some other graphics?  For example, I was working on a wedding website, and I found a lot of nice fonts for that subject. But I can't find the right way to add that font on the server. And how do I include that font with CSS into the HTML? Is this possible to do without graphics? Why does the Hilbert curve fill the whole square? How prove this $\prod_{1\le i<j\le n}\frac{a_{j}-a_{i}}{j-i}$ is integer Should I declare chocolate as "food" when entering the US? It is being customary we bring a few authentic Russian chocolate bars/sweets to the US but we are always struggling whether we should check that "food" checkbox in the "Customs Declaration" form?  It is under the following entry in the form (yeah, together with insects, right):     I am (We are) bringing:      fruits, vegetables, plants, seeds, food, insects   I've been always checking it but that just gets us into more lines and triggers extra questions after getting to the baggage check. Asymptote: when white isn't white I'm trying to display a white 3D ball with Asymptote (3D PDF), but it always turns up gray:    import graph3; import solids;  defaultrender.merge=true; size(10cm,0);  currentprojection=orthographic(-Z);  //currentlight=Headlamp; //currentlight=light(-10,1,1); //currentlight=White; currentlight=Viewport;  draw(unitsphere,rgb(1,1,1));   I understand it's a lighting issue, and I've tried playing with its settings (the lines commented out in my source are some of my attempts), but I never manage to have white be white. If I understand correctly, I need a whiter diffuse component in my light, but I cannot see how to achieve that. And the documentation is not very clear…    This will be part of a molecular model, and the rendering I'm going for it something like this: Prevent Adobe Reader from switching to "Fit Page" zoom when bookmark is clicked "Welcome to the Jones__": Plural or Plural Possessive? When making a welcome sign, what form of the name Jones would you use?  ("Welcome to the Jones__") What lies beyond the Sedenions How to know current name of the database in Django? Windows Server 2016 scheduled task schedule must be in future We have a 2012 server that has about 20 scheduled tasks that are used for monitoring.  We have built a 2016 server to replace it and as I move tasks to the new server I have run into an issue.  Most of our tasks run every few minutes.      In Server 2012 we would schedule the task to start at 1200AM of the current day (so a time in the past) and reoccur every X minutes.  The task would start at its next scheduled time.  Perfect.  In Server 2016 schedules that start in the past don't run.  So we had to schedule it to start in the future.  This is fine until you reboot.  Now the start time is in the past and it won't run.  It doesn't even register a failed run.  The Next Run Time column shows that it should run but doesn't.    Besides creating two triggers, one that starts in the future and another that starts on reboot (which we don't want to do since some tasks should only run at specified times), is there a better way?  This seems to be a bug.  The 2012 version worked great.  UPDATE  There is a workaround for this.  Create a one time schedule that runs indefinitely.  This works after restarts just like you would expect.  I know this isn't great for schedules that are "weird" but works fine for things that we want to run every 3 minutes or whatever. Log of products to sum of logs Is the phrase "for free" correct? I have a sword that currently rotates around a pivot point thats off of the actual object. Im new to blender and im not sure how i would go about changing it so that the sword rotates around the handle. Any help would be appreciated!