Mouse position inside autoscaled SVG

See this code, which not only shows how to transform from screen space to global SVG space, but also how to transform a point from SVG space into the transformed space of an element:
http://phrogz.net/svg/drag_under_transformation.xhtml

In short:

// Find your root SVG element
var svg = document.querySelector('svg');

// Create an SVGPoint for future math
var pt = svg.createSVGPoint();

// Get point in global SVG space
function cursorPoint(evt){
  pt.x = evt.clientX; pt.y = evt.clientY;
  return pt.matrixTransform(svg.getScreenCTM().inverse());
}

svg.addEventListener('mousemove',function(evt){
  var loc = cursorPoint(evt);
  // Use loc.x and loc.y here
},false);

Edit: I’ve created a sample tailored to your needs (albeit only in global SVG space):
http://phrogz.net/svg/rotate-to-point-at-cursor.svg

It adds the following method to the above:

function rotateElement(el,originX,originY,towardsX,towardsY){
  var angle = Math.atan2(towardsY-originY,towardsX-originX);
  var degrees = angle*180/Math.PI + 90;
  el.setAttribute(
    'transform',
    'translate('+originX+','+originY+') ' +
      'rotate('+degrees+') ' +
      'translate('+(-originX)+','+(-originY)+')'
  );
}